The density $\rho$ versus volume $V$ graph is shown in the figure. Find the corresponding pressure $P$ versus temperature $T$ graph.

$A$ thermodynamic process is shown in the figure. The pressures and volumes corresponding to some points in the figure are:
$P_A = 3 \times 10^4 \, Pa, \, P_B = 8 \times 10^4 \, Pa$ and $V_A = 2 \times 10^{-3} \, m^3, \, V_D = 5 \times 10^{-3} \, m^3$
In process $AB$,$600 \, J$ of heat is added to the system and in process $BC$,$200 \, J$ of heat is added to the system. The change in internal energy of the system in process $AC$ would be ...... $J$.

One mole of an ideal gas in initial state $A$ undergoes a cyclic process $ABCA$,as shown in the figure. Its pressure at $A$ is $P_0$. Choose the correct option$(s)$ from the following:
$(A)$ Internal energies at $A$ and $B$ are the same
$(B)$ Work done by the gas in process $AB$ is $P_0 V_0 \ln 4$
$(C)$ Pressure at $C$ is $\frac{P_0}{4}$
$(D)$ Temperature at $C$ is $\frac{T_0}{4}$

An ideal gas is taken through a quasi-static process described by $P = \alpha V^2$,where $\alpha = 5 \text{ atm}/m^6$. The gas is expanded to twice its original volume of $1 \text{ m}^3$. How much work is done by the expanding gas in this process?

An ideal monoatomic gas is taken through the thermodynamic states $A \to B \to C \to D$ via the paths shown in the figure. If $U_A, U_B, U_C$ and $U_D$ represent the internal energy of the gas in states $A, B, C$ and $D$ respectively,then which of the following is not true?

$A$ cyclic process for $1 \, \text{mol}$ of an ideal gas is shown in the $V-T$ diagram. Find the work done in processes $AB$,$BC$,and $CA$ respectively.