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

Two cylinders $A$ and $B$ fitted with pistons contain equal number of moles of an ideal monoatomic gas at $400 \,K$. The piston of $A$ is free to move while that of $B$ is held fixed. The same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $42 \,K$, what is the rise in temperature of the gas in $B$ (in $\,K$)? (Given $\gamma = 5/3$)

Consider that an ideal gas ($n$ moles) is expanding in a process given by $P = f(V)$,which passes through a point $(V_0, P_0)$. Show that the gas is absorbing heat at $(P_0, V_0)$ if the slope of the curve $P = f(V)$ is larger than the slope of the adiabatic curve passing through $(P_0, V_0)$.

An ideal monoatomic gas expands to twice its volume. If the process is isothermal,the magnitude of work done by the gas is $W_i$. If the process is adiabatic,the magnitude of work done by the gas is $W_a$. Which of the following is true?

An ideal gas undergoes a cyclic process through various thermodynamic states. The heat energy $(Q)$ and work $(W)$ associated with these states are given as follows:
$Q_1 = 6000 \ J, Q_2 = -5500 \ J, Q_3 = -3300 \ J, Q_4 = 3500 \ J,$
$W_1 = 2500 \ J, W_2 = -1000 \ J, W_3 = -1200 \ J, W_4 = x \ J$
If the ratio of the net work done to the net heat absorbed is $\eta$, then the values of $x$ and $\eta$ are respectively:

An ideal gas exists in a state with pressure $P_0$, volume $V_0$. It is isothermally expanded to $4$ times its initial volume $(V_0)$, then isobarically compressed to its original volume. Finally, the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is