Question

A gas for which $\gamma$ is $\frac{4}{3}$ is heated at constant pressure. The percentage of heat supplied used for external work is

• A. 25%
• B. 75 %
• C. 60 %
• D. 40 %

Answer 1

The correct option is A 25%

For a constant pressure heating process:
$dq=du+dw$
$n{C}_p\Delta T=n{C}_v\Delta T+nR\Delta T$

$\frac{\gamma R}{\gamma -1}=\frac{R}{\gamma -1}+R$

Fraction of heat supplied used for external work is:
$\frac{dw}{dq}=\frac{R}{\frac{R}{\gamma -1}+R}=\frac{\gamma -1}{\gamma }=\frac{\frac{4}{3}-1}{\frac{4}{3}}=0.25$

Percentage $=0.25\times 100=25$%