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 $: 1$)

For the combustion of $1 \ mol$ of liquid benzene at $298 \ K$,the heat of reaction at constant pressure is $-3268 \ kJ \ mol^{-1}$. What is the heat of combustion at constant volume? $(R = 8.314 \times 10^{-3} \ kJ \ K^{-1} \ mol^{-1})$

For the reaction:
$CH_{4(g)} + 2O_{2(g)} \to CO_{2(g)} + 2H_2O_{(l)}$;
$\Delta_r H_{300} = -212.7 \ Kcal/mol$.
The absolute value of $\Delta_r U_{300}^o$ for this reaction is ....... $Kcal/mol$ $(R = 2 \ cal/mol-K)$.

Match List-$I$ with List-$II$. Given $V_1$ and $V_2$ are initial and final volumes respectively.

List-$I$ (Isothermal process)	List-$II$ (Expression)
$A$. Reversible expansion	$I$. $q = 0$
$B$. Free expansion	$II$. $q = nRT \ln \frac{V_2}{V_1}$
$C$. Irreversible Compression	$III$. $w = -P_{ext}(V_1 - V_2)$
$D$. Cyclic reversible	$IV$. $\frac{q_{rev}}{T} = 0$

Match the following columns:

Column $I$	Column $II$
$(a)$ Adiabatic process	$(1)$ Heat
$(b)$ Isolated system	$(2)$ Constant volume
$(c)$ Isothermal change	$(3)$ First law of thermodynamics
$(d)$ Path function	$(4)$ No exchange of matter and energy
$(e)$ State function	$(5)$ No heat exchange
$(f)$ $\Delta U = q$	$(6)$ Constant temperature
$(g)$ Law of conservation of energy	$(7)$ Internal energy
$(h)$ Reversible process	$(8)$ $p_{ext} = 0$
$(i)$ Free expansion	$(9)$ Constant pressure
$(j)$ $\Delta H = q$	$(10)$ Infinitely slow process involving equilibrium states
$(k)$ Intensive property	$(11)$ Entropy
$(l)$ Extensive property	$(12)$ Pressure
	$(13)$ Specific heat

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 $R = 8.314 \ J \ mol^{-1} K^{-1}$]