Question

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

• A. 4$p_0{V}_0$
• B. 6$p_0{V}_0$
• C. 4.5$p_0{V}_0$
• D. 2$p_0{V}_0$

Answer 1

Answer: (B)

Change in internal energy from $A$ to $B$ is
$\Delta U=\frac{f}{2}\mu R\Delta T=\frac{f}{2}\left(p_f{V}_f-p_i{V}_i\right)$
$=\frac{3}{2}\left(2p_0\times 2V_0-p_0\times V_0\right)$
$=\frac{9}{2}{p}_0{V}_0$
Work done in process $A$ to $B$ is equal to the area covered by the graph with volume axis, ie,
$W_{A\to B}^{\prime }=\frac{1}{2}\left(p_0+2p_0\right)\times \left(2V_0-V_0\right)=\frac{3}{2}{p}_0{V}_0$
Hence, $\Delta Q=\Delta U+\Delta W$
$=\frac{9}{2}{p}_0{V}_0+\frac{3}{2}{p}_0{V}_0$
$=6p_0{V}_0$