For the reaction at $25^{\circ} C$, $X_2O_{4(l)} \longrightarrow 2 XO_{2(g)}$, $\Delta U$ and $\Delta S$ are $2.1 \ kCal$ and $20 \ cal \ K^{-1}$ respectively. What is $\Delta G$ for the reaction at the same temperature? $(R = 2 \ cal \ K^{-1} \ mol^{-1})$

The reaction of cyanamide,$NH_{2}CN_{(s)}$ with oxygen was run in a bomb calorimeter and $\Delta U$ was found to be $-742.24 \ kJ \ mol^{-1}$. The magnitude of $\Delta H_{298}$ for the reaction
$NH_{2}CN_{(s)} + \frac{3}{2} O_{2(g)} \rightarrow N_{2(g)} + CO_{2(g)} + H_{2}O_{(l)}$
is $............ \ kJ$. (Rounded off to the nearest integer)
[Assume ideal gases and $R = 8.314 \ J \ mol^{-1} K^{-1}$]

Consider the $P-V$ (pressure-volume) diagram given below,where an ideal gas is reversibly converted from state $X$ to state $Y$. Among the following,which is the correct $T-S$ (temperature-entropy) diagram corresponding to this process?

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	$(3)$ $\Delta S = (-)$

The standard molar heat of formation of ethane,$CO_2$,and water $(l)$ are respectively $-21.1$,$-94.1$,and $-68.3 \ kcal$. The standard molar heat of combustion of ethane will be $kcal$.

The ratio of heats liberated at $298 \ K$ from the combustion of one $kg$ of coke and by burning water gas obtained from $1 \ kg$ of coke is. (Assume coke to be $100 \%$ carbon.) (Given enthalpies of combustion of $CO_{2}, CO$ and $H_{2}$ as $393.5 \ kJ/mol, 283.5 \ kJ/mol, 285.5 \ kJ/mol$ respectively all at $298 \ K$.) (in $: 1$)