Question

The volume versus temperature graph of two moles of helium gas is shown in figure. The ratio of heat absorbed and the work done by the gas in process $1-2$ is

• A. $3$
• B. $\frac{5}{2}$
• C. $\frac{5}{3}$
• D. $\frac{7}{2}$

Answer 1

The correct option is B $\frac{5}{2}$

$V-T$ graph is a straight line passing through origin. Hence, $V\propto T$ or $P$ = constant.
$\therefore \Delta Q=n{C}_p\Delta T\mathrm{and}\Delta U=n{C}_v\Delta T$
$\mathrm{Also}\Delta W=\Delta Q-\Delta U=\mu (C_p-C_v)\Delta T$
$\therefore \frac{\Delta Q}{\Delta W}=\frac{n{C}_p\Delta T}{n(C_p-C_v)\Delta T}=\frac{C_p}{C_p-C_v}=\frac{1}{1-\frac{C_v}{C_p}}$
$\frac{C_v}{C_p}=\frac{3}{5}$ for helium gas. Hence
$\frac{\Delta Q}{\Delta W}=\frac{1}{1-3/5}=\frac{5}{2}$