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  4. If cp and cv denote the specific heats (per unit) mass of an ideal gas of molecular weight M, then where R is the molar gas constant.

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Q. If $c_p $ and $ c_v $ denote the specific heats (per unit) mass of an ideal gas of molecular weight $M$, then
where $R$ is the molar gas constant.

AIPMTAIPMT 2010Thermodynamics

Solution:

Let $C_v$ and $ C_p $ be molar specific heats of the ideal gas at constant volume and constant pressure, respectively, then
$C_p=Mc_p$ and $ C_v=Mc_v $
$C_P-C_V=R $
$\therefore Mc_p-Mc_v=R$
$\Rightarrow c_p-c_v=R/M $