The internal energy change (in $J$) when $90 \ g$ of water undergoes complete evaporation at $100^{\circ} C$ is........
(Given: $\Delta H_{vap}$ for water at $373 \ K = 41 \ kJ/mol$,$R = 8.314 \ J \ K^{-1} mol^{-1}$)

Standard entropies of $X_2, Y_2$ and $XY_3$ are $60, 40$ and $50 \ J \ K^{-1} \ mol^{-1}$ respectively. For the reaction $\frac{1}{2} X_2 + \frac{3}{2} Y_2 \rightleftharpoons XY_3, \Delta H = -30 \ kJ$,to be at equilibrium,the temperature should be ............. $K$.

Match the following terms in Column-$I$ with their corresponding descriptions in Column-$II$:

Column-$I$	Column-$II$
$(a)$ Adiabatic process	$(1)$ Heat
$(b)$ Isolated system	$(2)$ At 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	$(9)$ At constant pressure
$(j)$ $\Delta H = q$	$(10)$ Infinitely slow process involving multiple equilibrium states
$(k)$ Intensive property	$(11)$ Entropy
$(l)$ Extensive property	$(12)$ Pressure,$(13)$ Specific heat

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:

The heats of combustion of $C_{(s)}$,$H_{2(g)}$,and $C_{2}H_{6(g)}$ are $-x_{1}$,$-x_{2}$,and $-x_{3}$ respectively. The heat of formation of $C_{2}H_{6(g)}$ is:

$2.4 \ g$ 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)