# Ideal Gas and Thermodynamics

The question is :

Let M and N be specific heat at constant pressure and specific heat at constant volume.

M - N = a for hydrogen gas M - N = b for nitrogen gas

Then find the relation between a and b

By Mayor's Formula I did it as a=b but the correct answer is b = 14a. I need an explanation for it. Please help

You are messing up the molar specific heat and the specific heat, the former is per mole, and the latter is per kg.

For molar specific heat, we do have

$$C_P-C_V=R$$

But for specific heat we should use

$$c_P-c_V= \frac{1 \text{kg}}{\mu}R$$

where $\mu$ is the molar mass.

Note that for constant pressure and specific heat at constant volume, a and b depends on not only the type of gas, but also the molar mass.