Pressure versus volume graph of a monoatomic ideal gas is given. Find the internal energy of the system at 1 and amount of heat absorbed by the system during the process 4 to 1 .

$\mathrm{U}=\frac{3}{2}\mathrm{pV}\Rightarrow {\mathrm{U}}_1=\frac{3}{2}(2\times 1)=3\mathrm{J}$

Similarly ${\mathrm{U}}_2=22.5\mathrm{J},{\mathrm{U}}_3=37.5\mathrm{J}$

and ${\mathrm{U}}_4=15\mathrm{J}$

Work done during a process is given by area under $P-V$ curve.

$\begin{array}{l}{\mathrm{W}}_{12}=\frac{1}{2}(2+5)(3-1)=7\mathrm{J}\\ {\mathrm{W}}_{23}=5(5-3)=10\mathrm{J},{\mathrm{W}}_{34}=0\\ \text{ and }{\mathrm{W}}_{41}=-2(5-1)=-8\mathrm{J}\\ {\mathrm{Q}}_{41}=(\mathrm{\Delta U}{)}_{41}+{\mathrm{W}}_{41}=[3-15]\\ +[-8]=-20\mathrm{J}\end{array}$