The $\Delta H$ and $\Delta S$ for a reaction at $1 \ \text{atm}$ pressure are $+30.558 \ \text{kJ}$ and $0.066 \ \text{kJ K}^{-1}$ respectively. The temperature at which the free energy change will be zero and below this temperature the nature of the reaction would be:

State $1 \longleftarrow$ State $2 \longleftarrow$ State $3$
$\left(\begin{array}{c} T=300 \ K \\ P=15 \ bar \\ 1 \ mole \end{array}\right) \left(\begin{array}{c} T=300 \ K \\ P=10 \ bar \\ 1 \ mole \end{array}\right) \left(\begin{array}{c} T=300 \ K \\ P=5 \ bar \\ 1 \ mole \end{array}\right)$
The above shows a cyclic process. Calculate the total work done during one complete cycle. (Assume a single step to reach the next state).

The energy of combustion per mole of $H_2$,$LPG$,and octane follows the order:

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

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

Calculate the work done in $kJ$ when $3$ moles of an ideal gas at $27^{\circ} C$ expand isothermally and reversibly from $10 \ atm$ to $1 \ atm$ $[R=8.314 \ J \ K^{-1} \ mol^{-1}]$

Five moles of a gas are subjected to a series of changes as shown in the given graph. What are the processes $A \rightarrow B$,$B \rightarrow C$,and $C \rightarrow A$ respectively?