# Cp and Cv are specific heats at constant pressure and constant volume, respectively. It is observed that Cp − Cv =a for hydrogen gas Cp − Cv =b for nitrogen gas. The correct relation between a and b is :

In a system, Cp is the amount of heat energy released or absorbed by a unit mass of the substance with the change in temperature at a constant pressure.During a small change in the temperature of a substance, Cv is the amount of heat energy absorbed/released per unit mass of a substance where volume does not change.

The following relationship can be given considering the ideal gas behaviour of a gas. Cp – Cv = R

where R has been called universal gas constant.

For any gas, Cp−Cv = R, which is the gas constant.

Hence be it any gas, hydrogen or nitrogen, its value is same.

Here, for ideal gas, Cp – Cv = R/M, where M is the mass of one mole of gas.

Mass of one mole of hydrogen M=2 g and that of nitrogen M=28 g

∴ a=Cp−Cv=R/2 (for hydrogen)

And b=Cp−Cv=R/28 (for nitrogen)

⟹ a=14b

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