### Molar Specific Heats of Gas and Relation between Them

Molar specific heat of a gas at constant volume

The amount of the heat energy required to rise the temperature of unit mole of gas by 1°C at constant volume.

During this process the volume of the gas is Constant. As the volume is constant no external work is done in this process. According to first law thermodynamics all the heat energy supplied in this process is used only to increase the internal energy.

Molar specific heat of a gas at constant pressure

The amount of heat energy required to rise the temperature of unit mole of a gas by 1°C at constant pressure.

In this process the pressure of the system is kept constant. Here the heat energy supplied is used not only to increase the internal energy but also to do some external work.

It is obvious that Molar specific heat of a gas at constant pressure is greater than that of the Molar specific heat of a gas at constant volume.

Relation between two different specific heats of the gas

Basing on the very definition of the specific heats with can find the relation as shown below.

We also use first law Thermodynamics to derive the conclusion. It is proved below that the difference in the specific heats is equal to universal gas constant. It is constant for all the gases at all the conditions and the entire universe.

The same can be proved for the unit mass of the gas. But in this case you will be getting the difference between the specific heats as only gas constant which varies from one gas to another gas. That is the reason why mole is more standard in the nature while we are referring the gases than that of the mass in grams.

The ratio of specific heats depends on the nature of the gas.

For a Mono atomic gas its value is 5/3, for a diatomic gas its value is 7/ 5 and for a trial atomic gas its value is the 8 /6.

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