Third law of thermodynamics is law of entropy. It is a statement about the ability to create an absolute temperature scale, for which absolute zero is the point at which the internal energy of a solid is zero. Third law of thermodynamics states that it is impossible to reduce any system to absolute zero in a finite series of operations.
1.11 GAS LAWS
There are some relationships among temperature, volume, pressure, and quantity of a gas that could be described mathematically. This chapter deals with Boyle’s law, Charles’s law, Gay–Lussac’s law, and the combined gas law. These laws have one condition in common, i.e., fixed mass. In addition, some other properties of gases such as internal energy, specific heat capacity, and enthalpy have been introduced. Some of the important non-flow processes such as constant volume process, constant pressure process, isothermal processes, polytropic process, and adiabatic process have been explained with suitable examples. Some laws have been proposed by the various chemists such as Boyle’s law, Charle’s law, Gay–Lussac’s law based on the behaviour of ideal gases. These laws are discussed in the following subsections.
1.11.1 Boyle’s Law
Robert Boyle, a British chemist gave the first gas law, now known as Boyle’s law. This law describes the relationship between the pressure and volume of a sample of gas confined in a container. Boyle observed that when the pressure on an ideal gas is increased volume decreases. Similarly, when pressure is released the volume starts to increase. But Boyle’s law is true only when the temperature of the gas remains constant and no additional gas is added to the container or leaks out of the container. On the basis of these observations, the Boyle’s law is stated as: ‘that the volume and pressure of a sample of gas are inversely proportional to each other at constant temperature’.
This statement can be expressed as follows.
where V is volume and P is pressure.
For two different conditions 1 and 2, Boyle’s law can be expressed as
P1V1 = P2V2
where P1 and V1 are pressure and volume, respectively, at condition 1 and P2 and V2 are pressure and volume, respectively, at condition 2.
Example 1.25: A sample of nitrogen collected in the laboratory occupies a volume of 720 ml at a pressure of 1 atm. What volume will the gas occupy at a pressure of 2 atm, assuming the temperature remains constant?
Solution:
Given: V1 = 720 ml; P1 = 1 atm; P2 = 2 atm; V2 = ?
1.11.2 Charles’s Law
Jacques Charles carried out experiments on ideal gas and observed a relationship between the absolute temperature and volume of gases at constant pressure. Volume of the gas increases with increase in temperature and decreases with decrease in temperature. The Charle’s law can be stated as: ‘that the volume of a sample of gas is directly proportional to the absolute temperature when pressure remains constant’.
Charles’s law can be expressed as follows.
where V is volume and T is absolute temperature of the gas.
For two different conditions 1 and 2, Boyle’s law can be expressed as
where T1 and V1 are absolute temperature and volume, respectively, at condition 1 and T2 and V2 are absolute temperature and volume, respectively, at condition 2.
Example 1.26: A container of a gas has a volume of 360 ml at a temperature of 20°C. What volume will the gas occupy at 60°C?
Solution:
Given: V1 = 360 ml; T1 =273 + 20 = 293 K; T2 = 273 + 60 = 333 K; V2 = ?.
1.11.3 Gay–Lussac’s Law
Pressure of a confined gas increases with increasing temperature. If the temperature of the gas increases enough, the container can explode because of the pressure that builds up inside of it. The relationship between the pressure and temperature of a gas is described by Gay–Lussac’s law. ‘Gay–Lussac’s law states that the pressure of a sample of gas is directly proportional to the absolute temperature when volume remains constant’.
Gay–Lussac’s law can be expressed as follows.
where P is the pressure and T is the temperature of the gas.
For two different conditions 1 and 2, Gay–Lussac’s law can be expressed as
where T1 and P1 are absolute temperature and pressure, respectively, at condition 1 and T2 and P2 are absolute temperature and pressure, respectively, at condition 2.
Example 1.27: A cylinder of a gas has a pressure of 5 atm at 50°C. At what temperature in °C will it reach a pressure of 12 atm?
Solution:
Given: P1 = 5 atm; T1 =273 + 50 = 323 K; P2 = 12 atm; T2 = ?.
1.11.4 The Combined Gas Law
We have three different relationships among temperature, volume, and pressure of a gas; these are as follows:
Boyle’s Law: PV = k at constant temperature.
Charle’s Law: 
at constant pressure.
Gay–Lussac’s Law: 
at constant volume.
These three gas laws can be combined in one combined gas law. This law can be expressed as
Example 1.28: A sample of a gas has a volume of 80.0 ml at a pressure of 1 atm and a temperature of 20°C. What volume will the gas occupy at 1.5 atm and 45°C?
Solution:
Given: V1 = 80 ml; P1 = 1 atm; T1 = 273 + 20 = 293 K; P2 = 1.5 atm; T2 = 273 + 45 = 318 K; V2 = ?
1.11.5 Gas Constant
Since 1 mole of a gas occupies 22.4 l at standard temperature (273 K) and pressure (1 atm), it is possible to arrive at a mathematical expression to relate moles, pressure, temperature, and volume. This expression is called the ideal gas law. This law contains an additional term ‘R’ which is called the universal gas constant. In this expression ‘N’ equals the number of moles of a gas, the volume ‘V’ must be expressed in litres, the pressure ‘P’ must be expressed in atmospheres and the temperature must be expressed in degrees Kelvin.
This constant can be calculated by using the above values in this law.
When the values of 22.4 l and 273 degrees Kelvin are applied, the value of R is found to be
If we use CGS units, P will be expressed in dynes per square cm, V is the volume of a mole (i.e., the volume occupied by 6.0221 × 1023 molecules) and the value of the universal gas constant is 8.3145 × 107 erg/mole K. If we use SI units, P will be expressed in Pascal (N/m2), V will be the volume of a kilomole (i.e., the volume occupied by 6.0221 × 1026 molecules) and the value of the universal gas constant is 8.3145 × 103 J/kilomole K.
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