The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the figure. Which of the following statement$(s)$ is (are) correct?
$(A)$ $T_1 = T_2$
$(B)$ $T_3 > T_1$
$(C)$ $W_{\text{isothermal}} > W_{\text{adiabatic}}$
$(D)$ $\Delta U_{\text{isothermal}} > \Delta U_{\text{adiabatic}}$

$A$ pure substance (solid,liquid,or gas) of constant composition is taken in a closed container. Select the correct plot if pressure is applied at constant temperature in the absence of non-expansion work.

Three moles of an ideal gas are expanded isothermally from a volume of $300 \ cm^3$ to $2.5 \ L$ at $300 \ K$ against a constant external pressure of $1.9 \ atm$. The work done in joules is:

$A$ gas present in a cylinder expands against a constant pressure of $1 \, atm$ from a volume of $2 \, L$ to a volume of $6 \, L$. In doing so,it absorbs $800 \, J$ of heat from the surroundings. The change in internal energy of the process is ....... $J$.

$2.4 \ g$ coal is burnt in a bomb calorimeter in excess of oxygen at $298 \ K$ and $1 \ atm$ pressure. The temperature of the calorimeter rises from $298 \ K$ to $300 \ K$. The enthalpy change during the combustion of coal is $-x \ kJ \ mol^{-1}$. The value of $x$ is. (Nearest Integer) (Given: Heat capacity of bomb calorimeter $20.0 \ kJ \ K^{-1}$. Assume coal to be pure carbon)

Match the transformations in Column-$I$ with the appropriate options in Column-$II$.

Column-$I$	Column-$II$
$(A) \; CO_{2(s)} \to CO_{2(g)}$	$(p) \; \text{Transition state}$
$(B) \; CaCO_{3(s)} \to CaO_{(s)} + CO_{2(g)}$	$(q) \; \text{Allotropic change}$
$(C) \; 2H^{\cdot} \to H_{2(g)}$	$(r) \; \Delta H > 0$
$(D) \; P_{\text{(white solid)}} \to P_{\text{(red solid)}}$	$(s) \; \Delta S > 0$
	$(t) \; \Delta S < 0$