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

In the following figure,four curves $A, B, C$ and $D$ are shown. The curves are

Write the equation for the work done during the compression of an ideal gas.

Answer the following by appropriately matching the lists based on the information given in the paragraph.
In a thermodynamics process on an ideal monatomic gas,the infinitesimal heat absorbed by the gas is given by $T \Delta X$,where $T$ is the temperature of the system and $\Delta X$ is the infinitesimal change in a thermodynamic quantity $X$ of the system. For a mole of monatomic ideal gas,$X = \frac{3}{2} R \ln \left(\frac{T}{T_A}\right) + R \ln \left(\frac{V}{V_A}\right)$. Here,$R$ is the gas constant,$V$ is the volume of the gas,$T_A$ and $V_A$ are constants.
The $List-I$ below gives some quantities involved in a process and $List-II$ gives some possible values of these quantities.

List-$I$	List-$II$
$(I)$ Work done by the system in process $1 \rightarrow 2 \rightarrow 3$	$(P)$ $\frac{1}{3} R T_0 \ln 2$
$(II)$ Change in internal energy in process $1 \rightarrow 2 \rightarrow 3$	$(Q)$ $\frac{1}{3} R T_0$
$(III)$ Heat absorbed by the system in process $1 \rightarrow 2 \rightarrow 3$	$(R)$ $R T_0$
$(IV)$ Heat absorbed by the system in process $1 \rightarrow 2$	$(S)$ $\frac{4}{3} R T_0$
	$(T)$ $\frac{1}{3} R T_0 (3 + \ln 2)$
	$(U)$ $\frac{5}{6} R T_0$

If the process carried out on one mole of monatomic ideal gas is as shown in the figure in the $PV$-diagram with $P_0 V_0 = \frac{1}{3} R T_0$,the correct match is:
$(1)$ $I \rightarrow Q, II \rightarrow R, III \rightarrow P, IV \rightarrow U$
$(2)$ $I \rightarrow S, II \rightarrow R, III \rightarrow Q, IV \rightarrow T$
$(3)$ $I \rightarrow Q, II \rightarrow R, III \rightarrow S, IV \rightarrow U$
$(4)$ $I \rightarrow Q, II \rightarrow S, III \rightarrow R, IV \rightarrow U$
If the process on one mole of monatomic ideal gas is as shown in the $TV$-diagram with $P_0 V_0 = \frac{1}{3} R T_0$,the correct match is:
$(1)$ $I \rightarrow S, II \rightarrow T, III \rightarrow Q, IV \rightarrow U$
$(2)$ $I \rightarrow P, II \rightarrow R, III \rightarrow T, IV \rightarrow S$
$(3)$ $I \rightarrow P, II \rightarrow R, III \rightarrow Q, IV \rightarrow T$
$(4)$ $I \rightarrow P, II \rightarrow R, III \rightarrow T, IV \rightarrow P$
Give the answer for question $(1)$ and $(2)$.

$A$ monoatomic gas of pressure $P$ having volume $V$ expands isothermally to a volume $2V$ and then adiabatically to a volume $16V$. The final pressure of the gas is (ratio of specific heats $\gamma = \frac{5}{3}$)

Match the following:

Column $I$	Column $II$
$A$. Ratio of $\frac{\Delta Q}{\Delta U}$ in an isobaric process	$1$. $\frac{T_1}{T_1-T_2}$
$B$. Ratio of $\frac{\Delta Q}{\Delta W}$ in an isobaric process	$2$. $\frac{T_2}{T_1-T_2}$
$C$. Coefficient of performance of a refrigerator	$3$. $\frac{\gamma}{\gamma-1}$
$D$. Coefficient of performance of a heat pump	$4$. $\gamma$

Codes:
$A \quad B \quad C \quad D$