Three moles of an ideal gas $\left(C_{\mathrm{p}}=\frac{7}{2}R\right)$ at pressure $p_0$ and temperature $T_0$ is isothermally expanded to twice its initial volume. It is then compressed at a constant pressure to its original volume.
$\left(\mathrm{a}\right)$ Sketch $p-V$ and $p-T$ diagram for the complete process.
$\left(\mathrm{b}\right)$ Calculate not work done by the gas.
$\left(\mathrm{c}\right)$ Calculate net heat supplied to the gas during the complete process.

(Write your answer in terms of gas constant $R$)

An ideal monoatomic gas is confined by a spring-loaded massless piston of the cross-section $8.0\times {10}^{-3} {\mathrm{m}}^2$. Initially, the gas is at $300 \mathrm{K}$ and occupies a volume of $2.4\times {10}^{-3} {\mathrm{m}}^3$ and the spring is in its relaxed state. The gas is heated by an electric heater until the piston moves out slowly without friction by $0.1 \mathrm{m}$. Calculate

$\left(\mathrm{a}\right)$ the final temperature of the gas and
$\left(\mathrm{b}\right)$ the heat supplied by the heater. The force constant of the spring is $8000 \mathrm{N} {\mathrm{m}}^{-1}$, atmospheric pressure is $1.0\times {10}^5 \mathrm{N} {\mathrm{m}}^{-2}$. The cylinder and the piston are thermally insulated.