Question

In terms of mechanical unit, $C_P-C_V=\dots$ where $C_P$ and $C_V$ are principal specific heats.

• A. $2R$
• B. $\frac{R}{M}$
• C. $\frac{R}{J}$
• D. $\frac{R}{MJ}$

Answer 1

The correct option is C $\frac{R}{J}$

The relation between the specific heat of gas at constant volume and at a constant pressure was obtained by Robert Mayer in 1842.
$(C_P-C_V)dT=\frac{RdT}{J}$
or $C_P-C_V=\frac{R}{J}$
Note : If $C_P$ and $C_V$ are measured in the units of work and $R$ is also in the units of work (or energy), then the above relation becomes
$C_P-C_V=R$ .....(A)
For $1g$ of a gas, the relation will be
$C_P=C_V+\frac{R}{J}$
where $C_P$ and $C_V$ are specific heats and $R$ si gas constant for $1g$ of the gas.