Question

The $p-V$ diagram of $2 g$ of helium gas for a certain process $A \rightarrow B$ is shown in the figure. What is the heat given to the gas during the process $A \rightarrow B$ ?

• A. 4$p_0V_0$
• B. 6$p_0V_0$
• C. 4.5$p_0V_0$
• D. 2$p_0V_0$

Answer 1

Answer: (B)

Change in internal energy from $A$ to $B$ is
$\Delta U =\frac{f}{2} \mu R \Delta T=\frac{f}{2}\left(p_{f} V_{f}-p_{i} V_{i}\right) $
$=\frac{3}{2}\left(2 p_{0} \times 2 V_{0}-p_{0} \times V_{0}\right) $
$=\frac{9}{2} p_{0} V_{0}$
Work done in process $A$ to $B$ is equal to the area covered by the graph with volume axis, ie,
$W_{A \rightarrow B}^{\prime}=\frac{1}{2}\left(p_{0}+2 p_{0}\right) \times\left(2 V_{0}-V_{0}\right)=\frac{3}{2} p_{0} V_{0}$
Hence, $ \Delta Q=\Delta U+\Delta W$
$=\frac{9}{2} p_{0} V_{0}+\frac{3}{2} p_{0} V_{0}$
$=6 p_{0} V_{0}$