Question

A monoatomic gas expends at constant pressure on heating$.$ The percentage of heat supplied used for external work is

• A. $100\%$
• B. $40\%$
• C. $50\%$
• D. $70\%$

Answer 1

The correct option is B $40\%$

For an isobaric process$,$ $Q=n{C}_p\Delta TandW=nR\Delta T$

Now$,$ $C_p=\frac{\gamma R}{\gamma -1}$ for an isobaric process$,$ where $\gamma$ is the adiabatic index or the heat capacity ratio$.$

$\Rightarrow \frac{\Delta W}{\Delta Q}=\frac{R}{C_p}=\frac{\gamma -1}{\gamma }$

For monatomic gases$,$ $\gamma =\frac{5}{3}$

$\Rightarrow \frac{\Delta W}{\Delta Q}=\frac{\gamma -1}{\gamma }=\frac{\frac{5}{3}-1}{\frac{5}{3}}=0.4=40\%$

Hence,

option $\left(B\right)$ is correct answer.