Question

The volume $(V)$ of a monatomic gas varies with its temperature $(T)$, as shown in the graph. The ratio of work done by the gas, to the heat absorbed by it, when it undergoes a change from state $A$ to state $B$, is

• A. $\frac{2}{7}$
• B. $\frac{2}{5}$
• C. $\frac{1}{3}$
• D. $\frac{2}{3}$

Answer 1

Answer: (B)

$\frac{2}{5}$

Answer 2

Given process is isobaric
$dQ = n \,C_{p}\, dT$
$dQ = n\,\left(\frac{5}{2} R\right)\,dT$
$dW = P \,dV = n \,RdT$
Required ratio $= \frac{dW}{dQ} = \frac{nRdT}{n\left(\frac{5}{2}R\right)dT} = \frac{2}{5}$