Question

The difference between $C_p$ and $C_v$ can be derived from $H=U+PV$. Calculate the difference between $C_p$ and $C_v$ for 7.5 moles of an ideal gas.

• A. $82.36$ $Jmo{l}^{-1}{K}^{-1}$
• B. $72.36$ $Jmo{l}^{-1}{K}^{-1}$
• C. $62.36$ $Jmo{l}^{-1}{K}^{-1}$
• D. $52.36$ $Jmo{l}^{-1}{K}^{-1}$

Answer 1

The correct option is C $62.36$ $Jmo{l}^{-1}{K}^{-1}$

From first law, $\Delta U=q+w$
For a constant volume system, w = 0 and $\Delta U=n{C}_{v}dT$ = heat at constant volume
where n is the number of moles of the gas
Similarly, $\Delta H=n{C}_{p}dT$ = Heat at constant pressure
We know, $C_p-$ $C_v=nR$ for $n$ mole of a gas
$C_p-$ $C_v$ $=7.5\times 8.314$ $Jmo{l}^{-1}{K}^{-1}$
= $62.36$ $Jmo{l}^{-1}{K}^{-1}$