Question

When a diatomic gas expands at constant pressure, the percentage of heat supplied that increases temperature of the gas and in doing external work in expansion at constant pressure is

• A. $60\%$
• B. $40\%$
• C. $28.4$
• D. $71.42\%$

Answer 1

The correct option is B $40\%$

For an isobaric process$,$ $Q=n{C}_P\Delta T$ and $W=nR\Delta T$

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

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

For monotonic 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.