$C_p$ and $C_v$ are specific heats at constant pressure and constant volume respectively. It is observed that for hydrogen gas $C_p - C_v = a$ and for nitrogen gas $C_p - C_V = b$ . The correct relation between a and b is? [JEE mains 2017]

I applied Mayers relation and used $C_p - C_v=R$ for all gases, hence $a=b$ but that formula seems to be incorrect here. Supposedly, the correct mayer's relation is given as:

$$ C_p -C_v = \frac{R}{M}$$

Where $M$ is molar mass of gas in consideration.

I don't get how this equation came about. I had written a derivation for this Mayer's relation as a self answer (see here) in one of my old posts but I can't see where in the derivation missed a factor of molecular mass.

So, my question is where does molar mass of gas come into the formula of Mayer's relation from?

  • $\begingroup$ Is there a difference between the terms molar heat capacity and specific heat capacity? $\endgroup$ Commented Mar 9, 2021 at 21:24
  • $\begingroup$ Oh @ChetMiller I think I can self answer now $\endgroup$ Commented Mar 9, 2021 at 21:27

1 Answer 1


The thing to notice is that in the regular Mayer relation, the coefficients given are of specific heats (see here). So, if call the original molar quantites as $C_{p'}$ and $C_{v'}$, then:

$$C_p = \frac{C_{p'}}{M}$$


$$ C_v = \frac{C_{v'}}{M}$$

Hence, putting these back into the 'regular' mayer relation , we get the result.

Thanks to @Chet Miller for the hint


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.