$1 \, mol$ of oxygen gas is heated at constant volume from $20 \, ^oC$ to $30 \, ^oC$. What will be the change in the internal energy of the gas? Given the molar heat capacity of oxygen at constant pressure,$C_P = 7.03 \, cal \, mol^{-1} \, K^{-1}$ and $R = 2 \, cal \, mol^{-1} \, K^{-1}$. (Answer in $cal$)

Match the following processes with their corresponding entropy changes:

Process	Entropy Change
$(a)$ Liquid to vapor conversion	$(1)$ $\Delta S = 0$
$(b)$ Process not spontaneous at any temperature	$(2)$ $\Delta S = (+)$
$(c)$ Reversible expansion of an ideal gas	$(3)$ $\Delta S = (-)$

For an ideal gas, consider only $P-V$ work in going from an initial state $X$ to the final state $Z$. The final state $Z$ can be reached by either of the two paths shown in the figure. Which of the following choice(s) is (are) correct? [take $\Delta S$ as change in entropy and $w$ as work done].
(A) $\Delta S_{X \to Z} = \Delta S_{X \to Y} + \Delta S_{Y \to Z}$
(B) $w_{X \to Z} = w_{X \to Y} + w_{Y \to Z}$
(C) $w_{X \to Y \to Z} = w_{X \to Y} + w_{Y \to Z}$
(D) $\Delta S_{X \to Y \to Z} = \Delta S_{X \to Y}$

One mole of a monatomic ideal gas undergoes four thermodynamic processes as shown schematically in the $PV$-diagram below. Among these four processes,one is isobaric,one is isochoric,one is isothermal and one is adiabatic. Match the processes mentioned in List-$I$ with the corresponding statements in List-$II$.

List-$I$	List-$II$
$P$. In process $I$	$1$. Work done by the gas is zero
$Q$. In process $II$	$2$. Temperature of the gas remains unchanged
$R$. In process $III$	$3$. No heat is exchanged between the gas and its surroundings
$S$. In process $IV$	$4$. Work done by the gas is $6 P_0 V_0$

The standard entropies of $X_2, Y_2$ and $XY_3$ are $60, 40$ and $50 \ J \ K^{-1} \ mol^{-1}$ respectively. For the reaction $X_2 + 3Y_2 \rightleftharpoons 2XY_3; \Delta H = -60 \ kJ$ to be at equilibrium,the temperature should be.....$K$

How many quantities have a similar unit as molar entropy?
$(i)$ Heat capacity
$(ii)$ Molar heat capacity
$(iii)$ Universal gas constant
$(iv)$ Specific heat capacity