Consider the thermodynamic cycle shown on the $PV$ diagram. The process $A \rightarrow B$ is isobaric,$B \rightarrow C$ is isochoric,and $C \rightarrow A$ is a straight-line process. The following internal energy change and heat are given: $\Delta U_{A \rightarrow B} = + 400 \text{ kJ}$ and $Q_{B \rightarrow C} = - 500 \text{ kJ}$. The heat flow in the process $Q_{C \rightarrow A}$ is ...... $\text{kJ}$.

$A$ cyclic process on an ideal monatomic gas is shown in the figure. The correct statement is:

An ideal monoatomic gas is confined in a horizontal cylinder by a spring-loaded piston (as shown in the figure). Initially,the gas is at temperature $T_1$,pressure $P_1$,and volume $V_1$,and the spring is in its relaxed state. The gas is then heated very slowly to temperature $T_2$,pressure $P_2$,and volume $V_2$. During this process,the piston moves out by a distance $x$. Ignoring the friction between the piston and the cylinder,the correct statement$(s)$ is(are):
$(A)$ If $V_2=2V_1$ and $T_2=3T_1$,then the energy stored in the spring is $\frac{1}{4}P_1V_1$
$(B)$ If $V_2=2V_1$ and $T_2=3T_1$,then the change in internal energy is $3P_1V_1$
$(C)$ If $V_2=3V_1$ and $T_2=4T_1$,then the work done by the gas is $\frac{7}{3}P_1V_1$
$(D)$ If $V_2=3V_1$ and $T_2=4T_1$,then the heat supplied to the gas is $\frac{41}{6}P_1V_1$

One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where $V$ is the volume and $T$ is the temperature). Which of the statements below is (are) true?
$(A)$ Process $I$ is an isochoric process
$(B)$ In process $II$,gas absorbs heat
$(C)$ In process $IV$,gas releases heat
$(D)$ Processes $I$ and $III$ are $not$ isobaric

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

An ideal gas at pressure $P$ and volume $V$ is expanded to volume $2V$. Column $I$ represents the thermodynamic processes used during expansion. Column $II$ represents the work done during these processes in random order:

Column $I$	Column $II$
$(p)$ isobaric	$(x)$ $\frac{PV(1 - 2^{1 - \gamma})}{\gamma - 1}$
$(q)$ isothermal	$(y)$ $PV$
$(r)$ adiabatic	$(z)$ $PV \ln 2$

The correct matching of column $I$ and column $II$ is given by: