For the $P-V$ diagram of a thermodynamic cycle as shown in the figure,processes $BC$ and $DA$ are isothermal. Which of the corresponding graphs is correct?

Two moles of monoatomic gas is expanded from $(P_0, V_0)$ to $(P_0, 2V_0)$ under isobaric condition. Let $\Delta Q_1$,$\Delta W_1$,and $\Delta U_1$ be the heat given to the gas,the work done by the gas,and the change in internal energy,respectively. Now,the monoatomic gas is replaced by a diatomic gas,with other conditions remaining the same. The corresponding values in this case are $\Delta Q_2$,$\Delta W_2$,and $\Delta U_2$. Then:

$A$ heating element of resistance $r$ is fitted inside an adiabatic cylinder which carries a frictionless piston of mass $m$ and cross-sectional area $A$. The cylinder contains one mole of a diatomic gas. The temperature of the gas varies with time $t$ as $T = \alpha t + \frac{1}{2} \beta t^2$ (where $\alpha$ and $\beta$ are constants), while the pressure remains constant. The atmospheric pressure above the piston is $P_0$. Then:

One mole of a gas expands obeying the relation as shown in the $P-V$ diagram. The maximum temperature in this process is equal to

Two samples of gas $A$ and $B$ are initially at the same pressure and temperature. They are compressed from volume $V$ to $V/2$. If $A$ is compressed isothermally and $B$ is compressed adiabatically,then the final pressure of $A$ is:

Draw $P-V$ curves for isothermal and adiabatic processes of an ideal gas.