Calculate the difference between $\Delta H$ and $\Delta U$ for the following reaction at $25^{\circ} C$:
$C_2H_{6(g)} + 3.5O_{2(g)} \rightarrow 2CO_{2(g)} + 3H_2O_{(l)}$
(Given: $R = 8.314 \ J \ K^{-1} \ mol^{-1}$) (in $kJ$)

The $\Delta H$ for vaporisation of a liquid is $20 \, kJ/mol$. Assuming ideal behaviour,the change in internal energy for the vaporisation of $1 \, mole$ of the liquid at $60^{\circ} C$ and $1 \, bar$ is close to $.... \, kJ/mol$

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

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

$A$ calorimeter contains $0.2 \ kg$ of water at $30^{\circ} C$. $0.1 \ kg$ of water at $60^{\circ} C$ is added to it,the mixture is well stirred and the resulting temperature is found to be $35^{\circ} C$. The water equivalent of the calorimeter is $:-$ (in $J / K$)

Assertion : The increase in internal energy $(\Delta E)$ for the vaporization of one mole of water at $1 \ atm$ and $373 \ K$ is zero.
Reason : For all isothermal processes,$\Delta E = 0$.

At $300 \ K$,which of the following reactions with the given thermodynamic parameters occur spontaneously?