An ideal gas with pressure $P$, volume $V$ and temperature $T$ is expanded isothermally to volume $2V$ and a final pressure $P_i$. The same gas is expanded adiabatically to a volume $2V$ then the final pressure is $P_a$. In terms of $\gamma$, the ratio of the two specific heats for the gas, the ratio $P_i/P_a$ is

One mole of an ideal monoatomic gas is heated at a constant pressure of one atmosphere from $0^{\circ}C$ to $100^{\circ}C$. Then the change in the internal energy is

$A$ cyclic process $ABCA$ is shown in the $PT$ diagram. When presented on a $PV$ diagram,it would be:

In the given $P-V$ diagram,a monoatomic gas $\left(\gamma = \frac{5}{3}\right)$ is first compressed adiabatically from state $A$ to state $B$. Then it expands isothermally from state $B$ to state $C$. [Given: $\left(\frac{1}{3}\right)^{0.6} \simeq 0.5, \ln 2 \simeq 0.7$].
Which of the following statement$(s)$ is(are) correct?
$(A)$ The magnitude of the total work done in the process $A \rightarrow B \rightarrow C$ is $144 \text{ kJ}$.
$(B)$ The magnitude of the work done in the process $B \rightarrow C$ is $84 \text{ kJ}$.
$(C)$ The magnitude of the work done in the process $A \rightarrow B$ is $60 \text{ kJ}$.
$(D)$ The magnitude of the work done in the process $C \rightarrow A$ is zero.

An ideal gas is made to undergo a cycle depicted by the $p-V$ diagram given below. The curved line from $A$ to $B$ is an adiabat. Then,

$A$ cyclic process $ABCA$ is shown in the $V-T$ diagram. The corresponding process on the $P-V$ diagram is: