Two identical vessels $A$ and $B$ contain equal amounts of an ideal monoatomic gas. The piston of $A$ is fixed,while the piston of $B$ is free to move. The same amount of heat $\Delta Q$ is absorbed by both $A$ and $B$. If the internal energy of $B$ increases by $100 \, J$,what is the change in the internal energy of $A$ (in $, J$)?

An ideal gas is subjected to a cyclic process $A B C D$ as depicted in the $p-V$ diagram given below. Which of the following curves represents the equivalent cyclic process?

Carbon monoxide is carried around a closed cycle $abc$ in which $bc$ is an isothermal process as shown in the figure. The gas absorbs $7000 \; J$ of heat as its temperature increases from $300 \; K$ to $1000 \; K$ in going from $a$ to $b$. The quantity of heat rejected by the gas during the process $ca$ is ..... $J$. (in $; J$)

One mole of a diatomic ideal gas undergoes a process shown in $P-V$ diagram. The total heat given to the gas $(\ln 2 = 0.7)$ is (in $P_0 V_0$)

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.

$A$ heat engine is involved with an exchange of heat of $1915\, J,$ $-40\, J,$ $+125\, J,$ and $-Q\, J$ during one cycle,achieving an efficiency of $50.0 \%$. The value of $Q$ is ....... $J$.