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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

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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.

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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.

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