What are Specific Heat Capacities of Gases?

Gases express their absorbed energy in conditions of one gram of gas to raise its temperature by 1 degree Celsius as specific heat capacities. Specific heat capacity has two sub-classes called molar specific heat capacity at constant pressure and molar specific heat capacity at constant volume. Symbolically, they are represented as CP and CV, respectively. The specific heat capacity of gas may remain a little bit higher when it is allowed to expand since it is heated, i.e. represented as the specific heat capacity at constant pressure as compared to when it is heated in a closed vessel that stops its expansion, which is represented as the specific heat capacity at constant volume.

Heat Capacity

Heat capacity is simply defined as the amount of heat needed to involve changes in the heat content of 1 mole of a substance by an exact 10C.

What is Specific Heat Capacity?

Specific heat capacity for gas is the amount of energy required by one gram of gas to raise the temperature by unit degree Celsius. It is generally referred to as the heat capacity of gas and is also known as molar heat capacity when referred to in terms of moles of gas.

Mathematically, specific heat capacity is represented as- 

c=CM

Where c = specific heat capacity of the sample, C = heat capacity of a substance and M = mass of the sample.

Heat capacity is an extensive property since it depends on the mass of the substance. However, the specific heat capacity comes under the category of intensive properties. It has an intrinsic characteristic that does not show any dependence on the size or shape of the substance.

Specific heat values can be understood in the following way: 

When two materials that were initially present at varied temperatures come into contact with one another, the flow of heat will be from the warmer material towards the colder material. This will go on until both the materials attain the same temperature. It is already understood that when heat energy is absorbed by a substance, its temperature continues to increase. If the same quantity of heat is given to different substances having equal masses, then it is observed that the rise in temperature for each substance will be different.

Unit of Specific Heat Capacity

The SI unit of specific heat capacity for gases or other substances is given as – Joule per kelvin per kilogram i.e.

JK-1 Kg -1 or J/(KgK) or JK-1mol-1

Molar Specific Heat Capacity at Constant Pressure

Molar specific heat capacity at constant pressure for ideal monoatomic gases is defined as the amount of heat energy supplied to the sample when it is held at a constant pressure.

Mathematically, it can be represented as:

CP=52R      – – – – – – (1)

Molar Specific Heat Capacity at Constant Volume

Molar specific heat capacity at constant volume for monoatomic gases is defined as the amount of heat energy supplied to the sample of gases when it is held at a constant volume.

Mathematically, it can be represented as: 

CV=32R       – – – – – – – (2) 

The relation between equation (1) and (2) is:  

CP =CV+R

However, for polyatomic molecules under the category of diatomic or linear, it has been observed that two rotational degrees of freedom are added, which corresponds to the rotation about two perpendicular axes through the centre of the molecule. Thus, the formula would then be expected to give CV=52R, seen in gases like nitrogen and oxygen. Similarly, nonlinear polyatomic molecules will be able to rotate about three perpendicular axes, which in turn change the formula into CV=3R

Example of Specific Heat Capacities for Gases

Conclusion

Specific heat capacity for a gas is the amount of energy in the form of heat required by a unit mol of gas to raise the temperature by one degree Celsius. It is represented by the SI unit  JK-1 Kg -1 or J/(KgK) or JK-1mol-1. It is further divided into two classes as molar specific heat capacity at constant pressure and constant volume, represented by CP and CV, respectively.