“The mass and energy both are conserved in an isolated system”,is the statement of

For water at $100^{\circ} C$ and $1 \, bar$,$\Delta_{vap} H - \Delta_{vap} U = ...... \times 10^{2} \, J \, mol^{-1}$. (Round off to the Nearest Integer) $[Use : R = 8.31 \, J \, mol^{-1} \, K^{-1}]$ [Assume volume of $H_{2}O_{(\ell)}$ is much smaller than volume of $H_{2}O_{(g)}$. Assume $H_{2}O_{(g)}$ treated as an ideal gas]

For combustion of one mole of magnesium in an open container at $300 \ K$ and $1 \ bar$ pressure,$\Delta_{C}H^{\ominus} = -601.70 \ kJ \ mol^{-1}$,the magnitude of change in internal energy for the reaction is $.... \ kJ$. (Nearest integer)
(Given : $R = 8.3 \ J \ K^{-1} \ mol^{-1}$ )

$5 \, mol$ of an ideal gas expands isothermally and irreversibly from a pressure of $10 \, atm$ to $1 \, atm$ against a constant external pressure of $1 \, atm$. The work done $(w_{irr})$ at $300 \, K$ is:

For the reaction $CaCO_{3(s)} \rightarrow CaO_{(s)} + CO_{2(g)}$ at $977 \, ^\circ C$,$\Delta H = 174 \, kJ/mol$. Calculate $\Delta U$ in $kJ$.

$1 \, \text{mole}$ of an ideal gas is allowed to expand reversibly and adiabatically from a temperature of $27^{\circ}C$. The work done is $3 \, \text{kJ} \, \text{mol}^{-1}$. The final temperature of the gas is $...... \text{K}$ (Nearest integer). Given $C_{V} = 20 \, \text{J} \, \text{mol}^{-1} \, \text{K}^{-1}$.