Chemical Oxygen Demand (COD)

One problem with the BOD test is that it takes 5 days to run. If the organic compounds were oxidized chemically instead of biologically, the test could be shortened considerably. Such oxidation can be accomplished with the chemical oxygen demand (COD) test. Because nearly all organic compounds are oxidized in the COD test, while only some are decomposed during the BOD test, COD results are always higher than BOD results. The common compounds which cause COD to be higher than BOD include sulphides, sulphites, thiosulfates and chlorides. One example of this is wood pulping waste, in which compounds such as cellulose are easily oxidized chemically (high COD) but are very slow to decompose biologically (low BOD).

This test is carried out on the sewage to determine the extent of readily oxidizable organic matter, which is of two types.

1. Organic matter which can be biologically oxidized is called biologically active.
2. Organic matter which cannot be oxidized biologically is called biologically inactive.

COD gives the oxygen required for the complete oxidation of both biodegradable and non-biodegradable matter. COD is a measure of the oxygen equivalent of the organic matter content of a sample that is susceptible to oxidation by a strong chemical oxidant. It is an indirect method to measure the amount of organic compounds in water. It is expressed in milligrams per liter (mg/L), which indicates the mass of oxygen consumed per liter of solution.

The standard COD test uses a mixture of potassium dichromate and sulphuric acid to oxidize the organic matter (HCOH), with silver (Ag+) added as a catalyst. A simplified example of this reaction is illustrated below, using dichromate (Cr₂0₇^2-) and hydrogen ions (H+). A sample is refluxed in strongly acidic solution with a known excess of potassium dichromate (K₂Cr₂O₇) for 2-3 hours. After digestion, the remaining unreduced K₂Cr₂O₇ is titrated with ferrous ammonium sulphate to determine the amount of K₂Cr₂O₇ consumed. Then, the oxidizable matter is calculated in terms of oxygen equivalent. This procedure is applicable to COD values between 40 and 400 mg/L.

A known amount of a solution of K₂Cr₂O₇ in moderately concentrated sulphuric acid is added to a measured amount of sample and the mixture is boiled in air. In this reaction, the oxidizing agent, hexavalent chromium (Cr^VI), is reduced to trivalent chromium (Cr^III). After boiling, the remaining Cr^VI is titrated against a reducing agent, usually ferrous ammonium sulphate. The difference between the initial amount of Cr^VI added to the sample and the Cr^VI remaining after the organic matter has been oxidized is proportional to the chemical oxygen demand.

Total Organic Carbon

Since the ultimate oxidation of organic carbon is to CO₂, the total combustion of a sample yields some information about the potential oxygen demand in an effluent sample. A common application of total organic carbon testing is to assess the potential for creating disinfection by-products. Disinfection by-products are the result of halogens (e.g., bromine, chlorine) or ozone interacting with naturally occurring organic carbon compounds during the drinking water disinfection process. For example, trihalomethane, a carcinogen, is created when halogens displace three hydrogen ions on methane. Water that is high in total organic carbon has a greater potential to develop disinfection by-products. Some of the organics can be removed by adding levels of treatment specific for organic carbon absorption. It is usually not economically feasible to remove all naturally occurring organics from finished drinking water.

Total organic carbon is measured by oxidizing the organic carbon to CO₂ and H₂0 and measuring the CO₂ gas using an infrared carbon analyser. The oxidation is done by direct injection of the sample into a high-temperature (680-950°C) combustion chamber or by placing a sample into a vial containing an oxidizing agent such as potassium persulfate, sealing and heating the sample to complete the oxidation, then measuring the C02 using the carbon analyser.

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Biochemical Oxygen Demand (BOD)

The rate of oxygen use is commonly referred to as Biochemical Oxygen Demand (BOD). Biochemical Oxygen Demand is a chemical procedure for determining how fast biological organisms use up oxygen in a body of water. It is used in water quality management and assessment, ecology and environmental science. BOD is not an accurate quantitative test, although it is considered as an indication of the quality of a water source. Biochemical oxygen demand is not a specific pollutant, but rather a measure of the amount of oxygen required by bacteria and other microorganisms engaged in stabilizing decomposable organic matter over a specified period of time. The BOD test is often used to estimate the impacts of effluents that contain large amounts of biodegradable organics such as that from food processing plants and feedlots, municipal wastewater treatment facilities and pulp mills. A high oxygen demand indicates the potential for developing a dissolved oxygen sag as the microbiota oxidize the organic matter in the effluent. A very low oxygen demand indicates either clean water or the presence of a toxic or non-degradable matter.

The BOD test was first used in the late 1800s by the Royal Commission on Sewage Disposal as a measure of the amount of organic pollution in British rivers. At that time, the test was standardized to run for 5 days at 18.3⁰C. These numbers were chosen because none of the British rivers had headwater-to-sea travel times greater than 5 days and the average summer temperature for the rivers was 18.3⁰C. Accordingly, this should reveal the "worst case" oxygen demand in any British river. The BOD incubation temperature was later rounded to 20⁰C, but the 5-day test period remains the current as standard.

In its simplest version, the 5-day BOD test begins by placing water or effluent samples into two standard 60 - or 300 - mL BOD bottles (Fig.1). One sample is analysed immediately to measure the initial dissolved oxygen concentration in the effluent, often using a Winkler titration. The second BOD bottle is sealed and stored at 20°C in the dark. (The samples are stored in the dark to avoid photosynthetic oxygen generation). After 5 days the amount of dissolved oxygen remaining in the sample is measured. The difference between the initial and ending oxygen concentrations is the BOD.

Fig.1 Biochemical Oxygen Demand (BOD) Bottle

BOD is used in water quality management and assessment, ecology and environmental science. BOD is not an accurate quantitative test, although it is considered as an indication of the quality of a water source. It is most commonly expressed in milligrams of oxygen consumed per litre of sample during 5 days of incubation at 20°C or 3 days of incubation at 27°C. The BOD test must be inhibited to prevent oxidation of ammonia. If the inhibitor is not added, the BOD will be between 10% and 40% higher than can be accounted for by carbonaceous oxidation.

Stages of Decomposition in the BOD test

There are two stages of decomposition in the BOD test: a carbonaceous stage and a nitrogenous stage. The carbonaceous stage represents oxygen demand involved in the conversion of organic carbon to carbon dioxide. The second stage or the nitrogenous stage represents a combined carbonaceous plus nitrogenous demand, when organic nitrogen, ammonia and nitrite are converted to nitrate. Nitrogenous oxygen demand generally begins after about 6 days. Under some conditions, if ammonia, nitrite and nitrifying bacteria are present, nitrification can occur in less than 5 days. In this case, a chemical compound that prevents nitrification is added to the sample if the intent is to measure only the carbonaceous demand. The results are reported as carbonaceous BOD (CBOD) or as CBOD5 when a nitrification inhibitor is used.

BOD – Dilution Method

BOD is the amount of oxygen (Dissolved Oxygen (DO)) required for the biological decomposition of organic matter. The oxygen consumed is related to the amount of biodegradable organics. When organic substances are broken down in water, oxygen is consumed

              Organic Carbon + O₂ → CO2

Where, organic carbon in human waste includes protein, carbohydrates, fats, etc. Measure of BOD = Initial oxygen- Final Oxygen after (5 days at 20 °C) or (3 days at 27 °C). Two standard 300 mL BOD bottles are filled completely with wastewater. The bottles are sealed. Oxygen content (DO) of one bottle is determined immediately. The other bottle is incubated at 20°C for 5 days or (or at 27 °C for 3 days) in total darkness to prevent algal growth. After which its oxygen content is again measured. The difference between the two DO values is the amount of oxygen consumed by micro-organisms during 5 days and is reported as BOD5.

Where, DOi and DOf are initial and final DO concentrations of the diluted sample, respectively. P is called as dilution factor and it is the ratio of sample volume (volume of wastewater) to total volume (wastewater plus dilution water). 

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Water Quality - Biological Characteristics

The examination of water for the presence of bacteria is very important. The bacteria are very small organisms and it is not possible to detect them by microscopes. Hence, they are detected by circumstantial evidences or chemical reactions. The growth of bacteria takes place by cell division and there are various classifications of bacteria depending upon their shapes, oxygen requirements and effects on mankind. The last classification is important for the water supply engineer from the view point of public health. The bacteria may be harmless to mankind or harmful to mankind. The former category is known as non-pathogenic bacteria and the latter category is known as pathogenic bacteria. It is not possible to isolate pathogenic bacteria with the help of laboratory instruments. Their chances of presence in a sample of water are increased in relation to the amount of non-pathogenic bacteria present in the sample of water. The combined group of pathogenic and non-pathogenic bacteria is designated by Bacillus coli or B-coli group. This group of bacteria is present in the intestines of all living warm-blooded animals.

Water polluted by sewage contain one or more species of disease producing pathogenic bacteria. Pathogenic organisms cause water borne diseases and many non-pathogenic bacteria such as E.Coli, a member of coliform group, also live in the intestinal tract of human beings. Coliform itself is not a harmful group but it has more resistance to adverse condition than any other group. So, if it is ensured to minimize the number of coliforms, the harmful species will be very less. So, coliform group serves as indicator of contamination of water with sewage and presence of pathogens.

Many of the bacteria found in water are derived from air, soil and vegetation. Some of these are able to multiply and continue their existence while the remaining die out in due course of time. The selective medium that promote the growth of particular bacteria and inbuilt the growth of other organisms is used in the lab to detect the presence of the required bacteria, usually coliform bacteria. Following are the two standard bacteriological tests for bacteriological examination of water.

1. Total count or Agar plate count test

2. B-coli test

1) Total Count or Agar Plate Count Test

In this test, bacteria are cultivated on specially prepared medium of agar for different dilutions of sample of water with sterilized water. In this method total number of bacteria presents in a millitre of water is counted. 1 ml of sample water is diluted in 99ml of sterilized water and 1ml of dilute water is mixed with 10ml of agar of gelatine. The diluted sample is placed in an incubator for 24 hours at 37°C or for 48 hours at 20°C. After the sample will be taken out from the incubator and colonies of bacteria are counted by means of microscope. Drinking water should not have more than 10 coliforms/100ml.

2) B-coli Test

Sometimes this is also called as E–coli test. This test is divided into the following three parts.

1. Presumptive test

2. Confirmed test

3. Completed test

The presumptive test is based on the ability of coliform group to ferment the lactose broth and producing gas. The confirmed test consists of growing cultures of coliform bacteria on media which suppress the growth of other organisms. The completed test is based on the ability of the culture grown in the confirmed test to again ferment the lactose broth.

a) Presumptive Test

Following procedure is adopted in this test.

1. The definite amounts of diluted samples of water are taken in multiples of ten, such as 0.1 cc, 1.0 cc, 10 cc, etc.
2. The water is diluted in standard fermentation tubes containing lactose broth.
3. The tube is maintained at a temperature of 37°C for a period of 48 hours.
4. If gas is seen in the tube after this period is over, it indicates presence of B-coli group and the result of test is treated as positive. If reverse is the case, it indicates the absence of B-coli group and the result of test is treated as negative.
5. A negative result of presumptive test indicates that water is fit for drinking.

b) Confirmed Test

A small portion of lactose broth showing positive presumptive test is carefully transferred to another fermentation tube containing brilliant green lactose bile. If gas is seen in the tube after 48 hours, the result is considered positive and the completed test becomes essential.

c) Completed Test

This test is made by introducing or inoculating bacterial colonies into lactose broth fermentation tubes and agar tubes. The incubation is carried out at 37°C for 24 to 48 hours. If gas is seen after this period, it indicates positive result and further detailed tests are carried out to detect the particular type of bacteria present in water. The absence of gas indicates negative result and water is considered safe for drinking.

B-coli Index

This is an index or number which represents approximately the number of B-coli per cc of sample of water under consideration. The presumptive tests are carried out with different dilution ratios of the sample of water with sterilized water. A number of tests is carried out for each proportion and percentage of positive results is recorded. The difference between successive percentages is worked out and it is multiplied by the reciprocal of quantity of solution. The sum of such values indicates B-coli index. For potable water, B-coli index should be preferably less than 3 and it should not exceed 10 in any case.

M.P.N. Test (Most Probable Number)

It is the number which represents the bacterial density which is most likely to be present. The detection of bacteria by mixing different dilutions of a sample of water with fructose broth and keeping it in the incubator at 37°C for 48hours. The presence of acid or carbon dioxide gas in the test tube will indicate the presence of B-coli. After this the standard statistical tables (Maccardy’s) are referred and the “Most Probable Number” (MPN) of B-coli per 100ml of water are determined. For drinking water, the M.P.N. should not be more than 2.

Membrane Filter Technique

Now a days, a new technique of finding out the B-coli is developed which is called ‘Membrane Filter Technique”. This is a very simple method. In this method the sample of water is filtered through a sterilized membrane of special design due to which all the bacteria are retained on the membrane. The member is then put in contact of culture medium called M-Endo’s medium in the incubator for 24 hours at 37°C. The membrane after incubating is taken out and the colonies of bacteria are counted by means of microscope.

Coliform Index

Coliforms are the rod, shaped, non-pathogenic bacteria whose presence or absence in water indicates the presence or absence of faecal pollution. The total coliform group consists of members whose normal habitat is the lower portion of intestines of humans and warm and cold- blooded animals and soil. Some members which are not found in soil and vegetation constitute about 96% of all the coliforms of human faecal. Such members are called faecal coliforms. The total coliform group is widely used as an indicator organism of choice for drinking water. Escherichia coli (E-Coli) is the predominant member of the faecal coliform group. It is used to measure coliform bacteria present in water sample.

Water Borne Diseases

When water contains certain harmful and disease producing matter, it may lead to many diseases on being consumed by healthy persons. World health organization has observed that 80% of communicable diseases that are transmitted through water. The diseases like cholera, gastroenteritis, typhoid, diarrhoea, polio, hepatitis (Jaundice), Leptospirosis, Dracontiasis are caused by bacteria. Excess of fluorides present in water (above 1.5 mg/litre) cause diseases like dental fluorosis and skeletal fluorosis. This is a permanent irreversible disease that weakens the bone structure. The patient becomes immobile and bedridden.

Types of Water Borne Diseases

1) Common Cold and Flu

The disease that catches people across all of the age lines. When a person will get wet and may start constant sneezing, throat and fever are the severe symptoms of common cold and flu. It can be prevented by not getting in rain.

2) Dengue

The very common disease during rainy seasons. The virus is spread by the Aedes mosquito. The symptoms include high fever, pain in joints and muscles, vomiting, bleeding from nose, gums and even under skin due to haemorrhagic fever. It can be prevented by staying away from mosquitoes and clean the surroundings so that the mosquitoes don’t multiply.

3) Chikungunya

It is an another mosquito transmitted disease. The virus is spread by the Aedes Aegyptus mosquito. The symptoms include fever, swelling and stiffness of joints, muscular pain, headache, fatigue and nausea. It can be prevented by protecting from mosquito bites.

4) Cholera

It spreads through contaminated food, water and poor hygienic conditions. The symptoms include diarrhoea, vomiting, low blood pressure, dry mouth etc. It can be prevented by keeping drinking boiled water and maintain personal hygiene.

5) Typhoid Fever

The disease that spreads during the monsoon season. This disease is spread through contaminated food and water. The symptoms include prolonged fever, abdominal pain and headache. It can be prevented by getting a vaccination in advance and getting high intake of fluid to prevent dehydration.

Prevention of Waterborne Disease

• Improve quality and quantity of drinking at source, at the tap or in the storage vessel.
• Interrupt routes of spreading mosquitos by emptying accumulated water sources.
• Use chlorinated water
• Change hygiene behaviour, like hand washing
• Proper use of latrines
• Careful disposal of all waste products
• Proper maintenance of water supply, sanitation systems, pumps and wells
• Good food hygiene - wash before eating, protect from flies
• Improved immunizations practices, especially rotavirus
• Develop or enhance public health surveillance system
• Faster responses to emergent and dangerous pandemic strains of pathogenic infections
• Health education programs across the country

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Water Quality - Chemical Characteristics

1) pH value of Water/Hydrogen Ion Concentration

The acidity or alkalinity of water is measured in terms of its pH value or H-ion concentration. pH value is the logarithm of reciprocal of hydrogen ion activity in moles per litre. Depending upon the nature of dissolved salts and minerals, water may be acidic or alkaline. When acids or alkalis are dissolved in water, they dissociate into electrically charged hydrogen and hydroxyl radicals, respectively. pH of natural water is generally in the range of 6 - 8. Industrial wastes may be strongly acidic or basic and their effect on pH value of receiving water depends on the buffering capacity of receiving water. It is desirable to maintain pH value of water very close to 7. The acidic water causes tuberculation and the alkaline water causes incrustation. For potable water, the pH value should be between 7 and 8.50. Following are the two methods which are employed to measure the pH value of water.

a) Electrometric Method

In this method, potentiometer is used to measure the electrical pressure exerted by positively charged H-ions. The pH value is then correspondingly expressed.

b) Colourimetric Method

In this method, chemical reagents are added to water and the colour produced is compared with standard colours of known pH values. A set of sealed tubes containing coloured waters of known pH values is kept in the laboratory for ready reference. This test is simple and hence, it is commonly carried out in public health laboratories. The usual indicators are Benzol yellow, Methyl red, Bromphenol blue, etc., for acidic range and Thymol blue, Phenol red, Tolyl red, etc. for alkaline range.

2) Chlorides

The chloride contents, especially of sodium chloride or salt, are worked out for a sample of water. The excess presence of sodium chloride indicates pollution of water due to sewage, minerals, etc. and is dangerous and unfit for use. The water has lower contents of salt than sewage due to the fact that salt consumed in food is excreted by body. For potable water, the highest desirable level of chloride content is 200 mg/litre and its maximum permissible level is 600 mg per litre.

The natural waters near the mines and sea dissolve sodium chloride and also presence of chlorides may be due to mixing of saline water and sewage in the water. Sodium chloride is the main substance in chloride water. The natural water near the mines and sea has dissolved sodium chloride. Similarly, the presence of chlorides may be due to the mixing of saline water and sewage in the water. Excess of chlorides is considered as dangerous and makes the water unfit for many uses. Chloride content is determined by titrating the wastewater with silver nitrate and potassium chromate. Appearance of reddish colour confirms presence of chlorides in water. The measurement of chloride contents is carried out as follows.

1. 50 cc of sample of water is taken by pipette in a porcelain dish.
2. Two or three drops of potassium chromate solution are added to the sample of water.
3. The chloride content is then determined by titrating with standard solution of silver nitrate.
4. The silver reacts first with all chlorides and silver chloride thus formed then reacts with potassium chromate.
5. The silver chromate appears as reddish precipitate and the amount of silver nitrate required to produce such reddish precipitate determines the amount of chlorides present in water.

3) Dissolved Gases

The water contains various gases from its contact with the atmosphere and ground surfaces. The usual gases are nitrogen, methane, carbon dioxide and oxygen. In addition, water may contain some amount of hydrogen sulphide and ammonia depending upon the pH and anaerobic/aerobic condition of water. The contents of these dissolved gases in a sample of water are suitably worked out. The methane concentration is to be studied for its explosive property. The hydrogen sulphide gives disagreeable odour to water even if its amount is very small. The carbon dioxide content indicates biological activities, causes corrosion, increases solubility of many minerals in water and gives taste to water. Dissolved oxygen is necessary for sustenance of aquatic life in water and to keep it fresh. Oxygen in the dissolved state is obtained from atmosphere and pure natural surface water is usually saturated with it. The simple test to determine the amount of dissolved oxygen present in a sample of water is to expose water for 4 hours at a temperature of 27°C with 10% acid solution of potassium permanganate. The quantity of oxygen absorbed can then be calculated. This amount, for potable water, should be about 5 to 10 ppm.

4) Hardness

The hardness or soap-destroying power of water is of two types – temporary hardness and permanent hardness. The temporary hardness is also known as carbonate hardness and it is mainly due to the presence of bicarbonates of calcium and magnesium. It can be removed by boiling or by adding lime to the water. The permanent hardness is also known as non-carbonate hardness and it is due to the presence of sulphates, chlorides and nitrates of calcium and magnesium. It cannot be removed by simply boiling the water. It requires special treatment of water softening.

Total hardness = Carbonate hardness or alkalinity + Non carbonate hardness

The excess hardness of water is undesirable because of various reasons such as it causes more consumption of soap, affects the working of dyeing system, provides scales on boilers, causes corrosion and incrustation of pipes, makes food tasteless, etc. Presence of hardness in water prevents the lathering of the soap during cleaning of clothes, etc.

Hardness is usually expressed in mg of calcium carbonate per litre of water. Hardness is generally determined by Versenate Method. In this method, the water is titrated against EDTA salt solution using Eriochrome Black T as indicator solution. While titrating, colour changes from wine red to blue. In general, under a normal range of pH values, water with hardness up to 75 mg/L are considered as soft and those with 200 mg/L and above are considered as hard. In between, the water is considered as moderately hard. Underground water is generally harder than the surface water, as they have more opportunity to come in contact with minerals. For boiler feed water and for efficient cloth washing, etc., the water must be soft. However, for drinking purposes, water with hardness below 75 mg/L is generally tasteless and hence, the prescribed hardness limit for drinking ranges between 75 to 150 mg/L.

5) Alkalinity

The alkalinity is the capacity of a given sample to neutralize a standard solution of acid. The alkalinity is due to the presence of bicarbonate (HCO₃), carbonate (CO₃) or hydroxide (OH). The determination of alkalinity is very useful in waters and wastes because it provides buffering to resist changes in pH value. The alkalinity is usually divided into the following two parts. Total alkalinity i.e. above pH 4.5 and Caustic alkalinity i.e. above pH 8.2. The alkalinity is measured by volumetric analysis. The commonly adopted two indicators are given below.

1. Phenolphthalein : Pink above pH 8.5 and colourless below pH 8.2
2. Methyl Orange : Red below pH 4.5 and yellow orange above pH 4.5

6) Acidity

Acidity is a measure of the capacity of water to neutralise bases. Acidity is the sum of all titrable acid present in the water sample. Strong mineral acids, weak acids such as carbonic acid, acetic acid present in the water sample contributes to acidity of the water. Usually dissolved carbon dioxide (CO₂) is the major acidic component present in the unpolluted surface waters. The volume of standard alkali required to titrate a specific volume of the sample to pH 8.3 is called phenolphthalein acidity (Total Acidity). The volume of standard alkali required to titrate a specific volume of the water sample (wastewater and highly polluted water) to pH 3.7 is called methyl orange acidity (Mineral Acidity).

Acidity interferes in the treatment of water. Carbon dioxide is of important considerations in determining whether removal by aeration or simple neutralisation with lime /lime soda ash or NaOH will be chosen as the water treatment method. The size of the equipment, chemical requirements, storage spaces and cost of the treatment all depends on the carbon dioxide present. Aquatic life is affected by high water acidity. The organisms present are prone to death with low pH of water. High acidity water is not used for construction purposes. Especially in reinforced concrete construction due to the corrosive nature of high acidity water. Water containing mineral acidity is not fit for drinking purposes. Industrial wastewaters containing high mineral acidity is must be neutralized before they are subjected to biological treatment or direct discharge to water sources.

7) Total Solids

Total solids include suspended and dissolved solids. In this test, the amounts of dissolved and suspended matter present in water are determined separately and then added together to get the total amount of solids present in water. The highest desirable level of total solids is 500 mg/litre and its maximum permissible level is 1500 mg/litre. For measuring suspended solids, water is filtered through a fine filter and dry material retained on the filter is weighed. The filtered water is evaporated and weight of residue that remains on evaporation represents the amount of dissolved solids in water. Total solids can also be considered as the sum of organic and inorganic solids. Amount of inorganic solids can be determined by fusing the residue of total solids in a muffle-furnace and weighing the fused residue. Amount of organic solids is the difference between the amount of inorganic and total solid.

8) Nitrogen and its Compounds

The nitrogen is present in water in the following four forms. The presence of nitrogen in the water indicates the presence of organic maters in the water. 

• Free ammonia 
• Albuminoidal ammonia 
• Nitrites 
• Nitrates

The amount of free ammonia in potable water should not exceed 0.15 ppm and that of albuminoidal ammonia should not exceed 0.3 ppm. The term albuminoidal ammonia is used to represent the quantity of nitrogen present in water before decomposition of organic matter has started. The presence of nitrites indicates that the organic matter present in water is not fully oxidized or in other words, it indicates an intermediate oxidation stage. The amount of nitrites in potable water should be nil.

The presence of the nitrites in the water, due to partly oxidized organic matters, is very dangerous. Therefore, in no case nitrites should be allowed in the water. For potable water, the highest desirable level of nitrates is 45 mg per litre. The free ammonia is measured by simply boiling the water. The ammonia gas is then liberated. The albuminoidal ammonia is measured by adding strong alkaline solution of potassium permanganate to water and then boiling it. The ammonia gas is then liberated. The nitrites and nitrates are converted chemically into ammonia and then measured by comparison with standard colours. The nitrites are rapidly and easily converted to nitrates by the full oxidation of the organic matters. The presence of nitrates is not so harmful. But nitrates > 45 mg/L can cause “mathemoglobinemia” disease to the children.

9) Chlorine

Dissolved free chlorine is never found in natural waters. It is present in the treated water resulting from disinfection with chlorine. The chlorine remains as residual in treated water for the sake of safety against pathogenic bacteria. Residual chlorine is determined by the starch-iodide test. In starch-iodide test, potassium iodide and starch solutions are added to the sample of water due to which blue colour is formed. This blue colour is then removed by titrating with sodium thiosuplhate solution and the quantity of chloride is calculated. On the addition of ortho-iodine solution if yellow colour is formed, it indicates the presence of residual chlorine in the water. The intensity of this yellow colour is compared with standard colours to determine the quantity of residual chlorine. The residual chlorine should remain between 0.5 to 0.2 mg/L in the water so that it remains safe against pathogenic bacteria.

10) Iron and Manganese

These are generally found in ground water. The presence of iron and manganese in water makes it brownish red in colour. Presence of these elements leads to the growth of micro-organism and corrodes the water pipes. Iron and manganese also causes taste and odour in the water. The quantity of iron and manganese is determined by colorimetric methods.

11) Lead and Arsenic

These are not usually found in natural waters. But sometimes lead is mixed up in water from lead pipes or from tanks lined with lead paint when water moves through them. These are poisonous and dangerous to the health of public. The presence of lead and arsenic is detected by means of chemical tests.

Water contains various types of minerals and metals such as, copper, barium, cadmium, selenium, fluoride etc. Arsenic and selenium are poisonous; therefore, they must be removed totally. Human lungs are affected by the presence of high quantity of copper in the water. Fewer cavities in the teeth will be formed due to excessive presence of fluoride in water. The quantity of the metals and other substances can be done indirectly by colorimetric methods using UV-visible spectrophotometer or directly by the use of sophisticated instruments such as Atomic Absorption Spectrophotometer (AAS), Atomic Emission Spectrophotometer (AES), Inductively Coupled Mass Spectrophotometer (ICP-MS) etc.

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Characteristics of Concrete

Advantages of Concrete

a) Economical

Concrete is the most inexpensive and the most readily available material in the world. The cost of production of concrete is low compared with other engineered construction materials. The three major components in concrete are water, aggregate and cement. Compared with steel, plastics and polymers, these components are the most inexpensive and are available in every corner of the world. This enables concrete to be produced worldwide at very low cost for local markets, thus avoiding the transport expenses necessary for most other materials.

b) Ambient Temperature-Hardened Material

Because cement is a low-temperature bonded inorganic material and its reaction occurs at room temperature, concrete can gain its strength at ambient temperature. No high temperature is needed.

c) Ability to be Cast

Fresh concrete is flowable like a liquid and hence can be poured into various formworks to form different desired shapes and sizes right on a construction site. Hence, concrete can be cast into many different configurations.

d) Energy Efficient

Compared with steel, the energy consumption of concrete production is low. The energy required to produce plain concrete is only 450–750 kWh/ton and that of reinforced concrete is 800–3200 kWh/ton, while structural steel requires 8000 kWh/ton or more to make.

e) Excellent Resistance to Water

Unlike wood (timber) and steel, concrete can be hardened in water and can withstand the action of water without serious deterioration, which makes concrete an ideal material for building structures to control, store and transport water, such as pipelines, dams and submarine structures. Contrary to popular belief, water is not deleterious to concrete, even to reinforced concrete; it is the chemicals dissolved in water, such as chlorides, sulphates and carbon dioxide, that cause deterioration of concrete structures.

f) High-Temperature Resistance

Concrete conducts heat slowly and is able to store considerable quantities of heat from the environment. Moreover, the main hydrate that provides binding to aggregates in concrete, calcium silicate hydrate (C–S–H), will not be completely dehydrated until 910^oC. Thus, concrete can withstand high temperatures much better than wood and steel. Even in a fire, a concrete structure can withstand heat for 2–6 hours, leaving sufficient time for people to be rescued. This is why concrete is frequently used to build up protective layers for a steel structure.

g) Ability to Consume Waste

With the development of industry, more and more by-products or waste has been generated, causing a serious environmental pollution problem. To solve the problem, people have to find a way to consume such wastes. It has been found that many industrial wastes can be recycled as a substitute (replacement) for cement or aggregate, such as fly ash, slag (GGBFS = ground granulated blast-furnaces slag), waste glass and ground vehicle tires in concrete. Production of concrete with the incorporation of industrial waste not only provides an effective way to protect our environment, but also leads to better performance of a concrete structure. Due to the large amount of concrete produced annually, it is possible to completely consume most of industry waste in the world, provided that suitable techniques for individual waste incorporation are available.

h) Ability to Work with Reinforcing Steel

Concrete has a similar value to steel for the coefficient of thermal expansion (steel 1.2 × 10⁻⁵; concrete 1.0 – 1.5 × 10⁻⁵). Concrete produces a good protection to steel due to existence of CH and other alkalis (this is for normal conditions). Therefore, while steel bars provide the necessary tensile strength, concrete provides a perfect environment for the steel, acting as a physical barrier to the ingress of aggressive species and giving chemical protection in a highly alkaline environment (pH value is about 13.5), in which black steel is readily passivated.

i) Less Maintenance Required

Under normal conditions, concrete structures do not need coating or painting as protection for weathering, while for a steel or wooden structure, it is necessary. Moreover, the coatings and paintings have to be replaced few years. Thus, the maintenance cost for concrete structures is much lower than that for steel or wooden structures.

Limitations of Concrete

a) Quasi-Brittle Failure Mode

The failure mode of materials can be classified into three categories: brittle failure, quasi-brittle failure and ductile failure, as shown in Fig. 1. Glass is a typical brittle material. It will break as soon as its tension strength is reached. Materials exhibiting a strain-softening behaviour (Fig. 1-b) are called quasi-brittle materials. Both brittle and quasi-brittle materials fail suddenly without giving a large deformation as a warning sign. Ductile failure is a failure with a large deformation that serves as a warning before collapse, such as low-carbon steel. Concrete is a type of quasi-brittle material with low fracture toughness. Usually, concrete has to be used with steel bars to form so-called reinforced concrete, in which steel bars are used to carry tension and the concrete compression loads. Moreover, concrete can provide a structure with excellent stability. Reinforced concrete is realized as the second generation of concrete.

Fig.1 Three Failure Modes of Materials

b) Low Tensile Strength

Concrete has different values in compression and tension strength. Its tension strength is only about 1/10 of its compressive strength for normal-strength concrete or lower for high-strength concrete. To improve the tensile strength of concrete, fiber-reinforced concrete and polymer concrete have been developed.

c) Low Toughness (Ductility)

Toughness is usually defined as the ability of a material to consume energy. Toughness can be evaluated by the area of a load–displacement curve. Compared to steel, concrete has very low toughness, with a value only about 1/50 to 1/100 of that of steel, as shown in Fig. 2. Adding fibers is a good way to improve the toughness of concrete.

Fig.2 Toughness of Steel and Concrete

d) Low Specific Strength (Strength/Density Ratio)

For normal-strength concrete, the specific strength is less than 20, while for steel it is about 40. There are two ways to increase concrete specific strength: one is to reduce its density and the other is to increase its strength. Hence, lightweight concrete and high-strength concrete have been developed.

e) Formwork is Needed

Fresh concrete is in a liquid state and needs formwork to hold its shape and to support its weight. Formwork can be made of steel or wood. The formwork is expensive because it is labour intensive and time-consuming. To improve efficiency, precast techniques have been developed.

f) Long Curing Time

The design index for concrete strength is the 28-day compression strength. Hence, full strength development needs a month at ambient temperature. The improvement measure to reduce the curing period is steam curing or microwave curing.

g) Working with Cracks

Even for reinforced concrete structure members, the tension side has a concrete cover to protect the steel bars. Due to the low tensile strength, the concrete cover cracks. To solve the crack problem, prestressed concrete is developed and it is also realized as a third-generation concrete. Most reinforced concrete structures have existing cracks on their tension sides while carrying the service load.

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Flow Table Test

This is a laboratory test, which gives an indication of the quality of concrete with respect to consistency, cohesiveness and the proneness to segregation. This test is as per IS: 5512 – 1983. In this test, a standard mass of concrete is subjected to jolting. The spread or the flow of the concrete is measured and this flow is related to workability.

Flow Table Apparatus

The flow table top is constructed from a flat metal of minimum thickness 1.5 mm. The top is in plan 700 mm x 700 mm. The centre of the table is marked with a cross, the lines which run parallel to and out to the edges of the plate and with a central circle 200 mm in diameter. The front of the flow table top is provided with a lifting handle and the total mass of the flow table top is about 16 ± 1 kg. The flow table top is hinged to a base frame using externally mounted hinges in such a way that no aggregate can become trapped easily between the hinges or hinged surfaces.

Fig.1 Flow Table Apparatus

The front of the base frame shall extend a minimum 120 mm beyond the flow table top in order to provide a top board. An upper stop similar to that is provided on each side of the table so that the lower front edge of the table can only be lifted 40 ± 1mm. The lower front edge of the flow table top is provided with two hard rigid stops which transfer the load to the base frame. The base frame is so constructed that this load is then transferred directly to the surface on which the flow table is placed so that there is minimal tendency for the flow table top to bounce when allowed to fall.

Accessory Apparatus

Mould

The mould is made of metal readily not attacked by cement paste or liable to rust and of minimum thickness 1.5 mm. The interior of the mould is smooth and free from projections, such as protruding rivets and is free from dents. The mould shall be in the form of a hollow frustum of a cone having the internal dimensions as shown in Fig. 2. The base and the top is open and parallel to each other and at right angles to the axis of the cone. The mould is provided with two metal foot pieces at the bottom and two handles above them.

Fig. 2 Mould for Flow Test

Tamping Bar

The tamping bar is made of a suitable hardwood.

The table top is cleaned of all gritty material and is wetted. The mould is kept on the centre of the table, firmly held and is filled in two layers. Each layer is rodded 25 times with a tamping rod 1.6 cm in diameter and 61 cm long rounded at the lower tamping end. After the top layer is rodded evenly, the excess of concrete which has overflowed the mould is removed. The mould is lifted vertically upward and the concrete stands on its own without support. The table is then raised and dropped 12.5 mm 15 times in about 15 seconds. The diameter of the spread concrete is measured in about 6 directions to the nearest 5 mm and the average spread is noted. The flow of concrete is the percentage increase in the average diameter of the spread concrete over the base diameter of the mould.

The value could range anything from 0 to 150 per cent. A close look at the pattern of spread of concrete can also give a good indication of the characteristics of concrete such as tendency for segregation. As well as getting an accurate measurement of the workability of the concrete, the flow test gives an indication of the cohesion. A mix that is prone to segregation will produce a noncircular pool of concrete. Cement paste may be seen separating from the aggregate. If the mix is prone to bleeding, a ring of clear water may form after a few minutes.

Procedure

1. The table is made level and properly supported. Before commencing the test, the table-top and inner surface of the mould is wiped with a damp cloth.
2. The 700 mm square flow table is hinged to a rigid base, provided with a stop that allows the far end to be raised by 40 mm.
3. A cone, similar to that used for slump testing but truncated, is filled with concrete in two layers.
4. Each layer is tamped 10 times with a special wooden bar and the concrete of the upper layer finished off level with the top of the cone. Any excess is cleaned off the outside of the cone.
5. The cone is then raised allowing the concrete to flow out and spread out a little on the flow table.
6. The table top is then raised until it meets the stop and allowed to drop freely 15 times.
7. This causes the concrete to spread further, in a roughly circular shape.
8. The diameter of the concrete spread shall then be measured in two directions, parallel to the table edges.
9. The flow diameter is the average of the maximum diameter of the pool of concrete and the diameter at right angles.

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Vee-Bee Consistometer Test

This is a good laboratory test to measure indirectly the workability of concrete as per IS: 1199– 1959. The test equipment, which was developed by Swedish Engineer V. Bahrner, is shown in Fig.1. It consists of a vibrating table, a cylindrical pan, a slump cone and a glass or plastic disk attached to a free-moving rod, which serves as a reference endpoint. The cone is placed in the pan. After it is filled with concrete and any excessive concrete is struck off, the cone is removed. Then, the disk is brought into a position on top of the concrete cone and the vibrating table is set in motion and simultaneously a stop watch started. The vibration is continued till such a time as the conical shape of the concrete disappears and the concrete assumes a cylindrical shape. This can be judged by observing the glass disc from the top for disappearance of transparency. Immediately when the concrete fully assumes a cylindrical shape, the stop watch is switched off. The time required for the shape of concrete to change from slump cone shape to cylindrical shape in seconds is known as Vee Bee Degree. This method is very suitable for very dry concrete whose slump value cannot be measured by slump test but the vibration is too vigorous for concrete with a slump greater than about 50 mm.

The Vee bee test is a good laboratory test, particularly for very dry mixes. This is in contrast to the compacting factor test where error may be introduced by the tendency of some dry mixes to stick in the hoppers. The Vee bee test also has the additional advantage that the treatment of concrete during the test is comparatively closely related to the method of placing in practice. Moreover, the cohesiveness of concrete can be easily distinguished by Vee bee test through the observation of distribution of the coarse aggregate after vibration. Table 1 shows the relationship between workability and Vee Bee values.

Fig.1 Vee bee Test Setup

Procedure

1. Mix the dry ingredients of the concrete thoroughly till a uniform colour is obtained and then add the required quantity of water.
2. Pour the concrete into the slump cone with the help of the funnel fitted to the stand.
3. Remove the slump mould and rotate the stand so that transparent disc touches the top of the concrete.
4. Start the vibrator on which cylindrical container is placed.
5. Due to vibrating action, the concrete starts remoulding and occupying the cylindrical container. Continue vibrating the cylinder till concrete surface becomes horizontal.
6. The time required for complete remoulding in seconds is the required measure of the workability and it is expressed as number of Vee-bee seconds.

Table 1 Relationship between Workability and Vee Bee Test Results

Workability Description	Vee-bee Time in Seconds
Extremely dry	32 – 18
Very stiff	18 – 10
Stiff	10 – 5
Stiff plastic	5 – 3
Plastic	3 – 0
Flowing	-

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Kelly Ball Test

This is a simple field test consisting of the measurement of the indentation made by 15 cm diameter metal hemisphere weighing 13.6 kg connected to a handle with a ruler, when freely placed on fresh concrete. ASTM C360 covers the Kelly ball penetration test. The hammer is fixed on a box container through a pin. When taking measurements, the box is placed on the top of the concrete to be tested with the surface of the hammer touching the concrete. When the pin is removed, the hammer will sink into the fresh concrete by its own weight. The depth of the hammer penetration can be read from the ruler and is used as an index of workability. A concrete with higher consistency leads to a deeper ball penetration. The penetration test is usually very quick and can be done on site, right in the formwork, provided it is wide enough. The ratio of slump value to penetration depth is from 1.3 to 2.0.

The test has been devised by Kelly and hence known as Kelly Ball Test. This has not been covered by Indian Standards Specification. The advantages of this test is that it can be performed on the concrete placed in site and it is claimed that this test can be performed faster with a greater precision than slump test. The disadvantages are that it requires a large sample of concrete and it cannot be used when the concrete is placed in thin section. The minimum depth of concrete must be at least 20 cm and the minimum distance from the centre of the ball to nearest edge of the concrete is 23 cm. The surface of the concrete is struck off level, avoiding excess working, the ball is lowered gradually on the surface of the concrete. The depth of penetration is read immediately on the stem to the nearest 6 mm. The test can be performed in about 15 seconds and it gives much more consistent results than Slump Test.

Fig. 1 Kelly Ball Apparatus

Test Procedure

• The concrete which is presumed to be tested should be poured into a container such as a buggy or actually in the form which should be up to a depth of 200mm (20cm). Then once the concrete is poured the top surface should be levelled.
• On the surface of the concrete the Kelly ball apparatus should be placed. The handles of the hemisphere (ball) should be placed in such a way that the frame touches the surface of the concrete. Away from the containers end the minimum lateral dimension of frame should be around 230 mm (23 cm).
• Then once it is done, the handle should be released slowly and the ball should be allowed to penetrate through the concrete by its own weight.
• Once the ball (hemisphere) is relieved, the penetration depth of the ball will be signified on the scale.
• Then the reading of the graduated scale should be noted down. (in which the penetration is showed).

The same procedure should be repeated at different portions for at least three times in the container and the then the average values of these readings should be taken down.

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Compaction Factor Test

The compacting factor test is designed primarily for use in the laboratory but it can also be used in the field. It is more precise and sensitive than the slump test and is particularly useful for concrete mixes of very low workability as are normally used when concrete is to be compacted by vibration. Such dry concrete is insensitive to slump test. The compacting factor test has been developed at the Road Research Laboratory U.K. and it is claimed that it is one of the most efficient tests for measuring the workability of concrete. This test works on the principle of determining the degree of compaction achieved by a standard amount of work done by allowing the concrete to fall through a standard height.

The degree of compaction, called the compacting factor is measured by the density ratio i.e., the ratio of the density actually achieved in the test to density of same concrete fully compacted. The sample of concrete to be tested is placed in the upper hopper up to the brim. The trap-door is opened so that the concrete falls into the lower hopper. Then the trap-door of the lower hopper is opened and the concrete is allowed to fall into the cylinder. In the case of a dry-mix, it is likely that the concrete may not fall on opening the trap-door. In such a case, a slight poking by a rod may be required to set the concrete in motion. The excess concrete remaining above the top level of the cylinder is then cut off with the help of plane blades supplied with the apparatus. The outside of the cylinder is wiped clean. The concrete is filled up exactly up to the top level of the cylinder. It is weighed to the nearest 10 grams. This weight is known as ―Weight of partially compacted concrete.

The cylinder is emptied and then refilled with the concrete from the same sample in layers approximately 5 cm deep. The layers are heavily rammed or preferably vibrated so as to obtain full compaction. The top surface of the fully compacted concrete is then carefully struck off level with the top of the cylinder and weighed to the nearest 10 gm. This weight is known as Weight of fully compacted concrete. Usually, the range of compaction factor is from 0.78 to 0.95 and concrete with high fluidity has a higher compaction factor.

Theory

This test is adopted to determine workability of concrete where nominal size of aggregate does not exceed 40 mm and it is as per IS: 1199 – 1959. It is based on the definition, that workability is that property of concrete, which determines the amount of work required to produce full compaction. The test consists essentially of applying a standard amount of work to standard quantity of concrete and measuring the resulting compaction. The compaction factor is defined as the ratio of the weight of partially compacted concrete to the weight of fully compacted concrete. It shall be stated to the nearest second decimal place. The relationship between degree of workability and compaction factor are given below.

Table 1 Relationship between Degree of workability and Compaction Factor

Degree of workability	Compaction Factor
Very Low	0.75- 0.80
Low	0.80- 0.85
Medium	0.85- 0.92
High	> 0.92

Compaction factor test is more sensitive and precise than slump test and is particularly useful for concrete mixes of very low workability. Such concrete may show zero to very low slump value. Also, compaction factor (C.F.) test is able to indicate small variations in workability over a wide range. Compaction factor test proves the fact that with increase in the size of coarse aggregate, the workability will decrease. However, compaction factor test has certain limitations. When maximum size of aggregate is large as compare with mean particle size; the drop into bottom container will produce segregation and give unreliable comparison with other mixes of smaller maximum aggregate sizes. Moreover, the method of introducing concrete into mould bears no relationship to any of the more common methods of placing and compacting high concrete.

Compaction Factor Test Apparatus

Compaction factor test apparatus consists of two conical hoppers, A and B, mounted vertically above a cylindrical mould C. The upper hopper A has internal dimensions as: top diameter 250 mm; bottom diameter 125 mm and height 225 mm. The lower hopper B has internal dimensions as: top diameter 225 mm; bottom diameter 125 mm and height 225 mm. The cylinder has internal dimensions as: 150 mm diameter and 300 mm height. The distances between bottom of upper hopper and top of lower hopper, and bottom of lower hopper and top of cylinder are 200 mm in each case. The lower ends of the hoppers are fitted with quick release flap doors. The hoppers and cylinders are rigid in construction and rigidly mounted on a frame. These hoppers and cylinder are rigid and easily detachable from the frame. Other instruments used for this test consists of trowels, hand scoop (15.2 cm long), a rod of steel or other suitable material (1.6 cm diameter, 61 cm long rounded at one end) and a balance.

Fig.1 Compaction Factor Test Apparatus

Procedure

1. Prepare a concrete mix for testing workability. Consider a W/C ratio of 0.5 to 0.6 and design mix of proportion about 1:2:4 (it is presumed that a mix is designed already for the test). Weigh the quantity of cement, sand, aggregate and water correctly. Mix thoroughly. Use this freshly prepared concrete for the test.
2. Place the concrete into the upper hopper up to its brim.
3. Open the trapdoor of the upper hopper. The concrete will fall into the lower hopper.
4. Open the trapdoor of the lower hopper, so that concrete falls into the cylinder below.
5. Remove the excess concrete above the level of the top of the cylinder; clean the outside of the cylinder.
6. Weigh the concrete in the cylinder. This weight of concrete is the "weight of partially compacted concrete", (W1).
7. Empty the cylinder and refill with concrete in layers, compacting each layer well (or the same may be vibrated for full compaction). Top surface may be struck off level.
8. Find cut weight of the concrete in the fully compacted state. This weight is the “Weight of fully compacted concrete" (W2).

The degree of compaction, called the compacting factor is measured by the density ratio i.e., the ratio of the density actually achieved in the test to density of same concrete fully compacted.

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Equation of State: The Perfect Gas

The assumed properties of a perfect gas are closely matched by those of actual gases in many circumstances, although no actual gas is perfect. The molecules of a perfect gas would behave like tiny, perfectly elastic spheres in random motion and would influence one another only when they collided. Their total volume would be negligible in comparison with the space in which they moved. From these hypotheses the kinetic theory of gases indicates that, for equilibrium conditions, the absolute pressure p, density ‘ρ’, the volume V occupied by mass m and the absolute temperature T are related by the expression

p = ρRT

                                                                              or           pV = mRT                      (1)

in which ‘R’ is a constant called the gas constant, the value of which is constant for the gas concerned and ‘V’ is the volume occupied by the mass m of the gas. The absolute pressure is the pressure measured above absolute zero (or complete vacuum) and is given by

p_abs = p_gage + p_atm 

The absolute temperature is expressed in ‘kelvin’ i.e., K, when the temperature is measured in °C and it is given by

T°(abs) = T K = 273.15 + t°C

No actual gas is perfect. However, most gases (if at temperatures and pressures well away both from the liquid phase and from dissociation) obey this relation closely and hence their pressure, density and (absolute) temperature may to a good approximation, be related by Eq.1.

Similarly, air at normal temperature and pressure behaves closely in accordance with the equation of state. It may be noted that the gas constant R is defined by Eq. 1 as p/ρT and therefore, its dimensional expression is (FL/Mθ). Thus in SI units the gas constant R is expressed in Newton-metre per kilogram per kelvin i.e., (N.m/kg. K). Further, since 1 joule = 1 newton × 1 metre, the unit for R also becomes joule per kilogram per kelvin i.e., (J/kg. K). Again, since 1 N = 1 kg × 1 m/s², the unit for R becomes (m²/s² K).

In metric gravitational and absolute systems of units, the gas constant R is expressed in kilogram (f)-metre per metric slug per degree C absolute i.e., [kg(f)-m/msl deg. C abs.] and dyne-centimetre per gram (m) per degree C absolute i.e., [dyne-cm/gm(m) deg. C abs.] respectively. For air the value of R is 287 N-m/kg K, or 287 J/kg K, or 287 m²/s² K.

In metric gravitational system of units, the value of R for air is 287 kg(f)-m/msl deg. C abs. Further, since 1 msl = 9.81 kg (m), the value of R for air becomes (287/9.81) or 29.27 kg(f)-m/kg(m) deg. C abs.

Since specific volume may be defined as reciprocal of mass density, the equation of state may also be expressed in terms of specific volume of the gas as

pv = RT

in which v is specific volume.

The equation of state may also be expressed as

p = wRT

in which w is the specific weight of the gas. The unit for the gas constant R then becomes (m/K) or (m/deg. C abs). It may be shown that for air the value of R is 29.27 m/K. For a given temperature and pressure, Eq. 1 indicates that ρR = constant. By Avogadro’s hypothesis, all pure gases at the same temperature and pressure have the same number of molecules per unit volume. The density is proportional to the mass of an individual molecule and so the product of R and the ‘molecular weight’ M is constant for all perfect gases. This product MR is known as the universal gas constant. For real gases it is not strictly constant but for monatomic and diatomic gases its variation is slight. If M is the ratio of the mass of the molecule to the mass of a hydrogen atom, MR = 8310 J/kg K.

Any equation that relates p, ρ and T is known as an equation of state and equation of state is therefore termed the equation of state of a perfect gas. Most gases, if at temperatures and pressures well away both from the liquid phase and from dissociation, obey this relation closely and so their pressure, density and (absolute) temperature may, to a good approximation, be related by Eqn. 1. For example, air at normal temperatures and pressures behaves closely in accordance with the equation. But gases near to liquefaction – which are then usually termed vapours – depart markedly from the behaviour of a perfect gas. Equation 1 therefore does not apply to substances such as non-superheated steam and the vapours used in refrigerating plants. For such substances, corresponding values of pressure, temperature and density must be obtained from tables or charts.

It is usually assumed that the equation of state is valid not only when the fluid is in mechanical equilibrium and neither giving nor receiving heat, but also when it is not in mechanical or thermal equilibrium. This assumption seems justified because deductions based on it have been found to agree with experimental results.

Calorically Perfect Gas

A gas for which the specific heat capacity at constant volume, cv, is a constant is said to be calorically perfect. The term perfect gas, used without qualification, generally refers to a gas that is both thermally and calorically perfect.

Changes of State

A change of density may be achieved both by a change of pressure and by change of temperature. If the process is one in which the temperature is held constant, it is known as isothermal. On the other hand, the pressure may be held constant while the temperature is changed. In either of these two cases there must be a transfer of heat to or from the gas so as to maintain the prescribed conditions. If the density change occurs with no heat transfer to or from the gas, the process is said to be adiabatic.

If, in addition, no heat is generated within the gas (e.g. by friction) then the process is described as isentropic, and the absolute pressure and density of a perfect gas are related by the additional expression p/e^γ  = constant, where γ = cp/cv and cp and cv represent the specific heat capacities at constant pressure and constant volume respectively. For air and other diatomic gases in the usual ranges of temperature and pressure γ = 1.4.

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