The P-V diagram of 4 gm 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   $A\to B$

Change in internal energy from $A\to B$  is 

$\begin{array}{l}\Delta U=\frac{f}{2}\mu R\Delta T=\frac{f}{2}(P_f{V}_f-P_i{V}_i)\\ =\frac{3}{2}(2P_0\times 2V_0-P_0\times V_0)=\frac{9}{2}{P}_0{V}_0\end{array}$

Work done in process  $A\to B$ is equal to the Area covered by the graph with volume axis i.e.,

$W_{A\to B}=\frac{1}{2}(P_0+2P_0)\times (2V_0-V_0)=\frac{3}{2}{P}_0{V}_0$

$Hence, \Delta Q=\Delta U+\Delta W =\frac{9}{2}{P}_0{V}_0+\frac{3}{2}{P}_0{V}_0=6P_0{V}_0$