One mole of water is converted into steam at $373 \, K$. The heat absorbed at $1 \, atm$ pressure is $40.68 \, kJ$. If the molar volumes of water and steam are $18 \, mL$ and $30600 \, mL$ respectively,find $\Delta U$ for the process in $kJ$.

$7 \ g$ of $N_{2(g)}$ at $27 \ ^oC$ is expanded reversibly and isothermally from an initial pressure of $0.5 \ MPa$ to a final pressure of $0.1 \ MPa$. Determine the approximate work done $[\ln \ 5 = 1.6]$ ..... $J$

For a reaction,$X_{2(g)} + Y_{2(g)} \rightleftharpoons 2XY_{(g)}$. If $\Delta G_r^o = 20 \ kJ \ mol^{-1}$ and $\Delta S_r^o = -20 \ J \ K^{-1} \ mol^{-1}$ at $200 \ K$. Calculate $\Delta H_r^o$ at $400 \ K$ (Given $\Delta_r C_P = 20 \ J \ K^{-1} \ mol^{-1}$).

$36 \, mL$ of pure water takes $100 \, sec$ to evaporate from a vessel and heater connected to an electric source which delivers $806 \, watt$. The $\Delta H_{\text{vaporization}}$ of $H_2O$ is $... \, kJ/mol$

Calculate the enthalpy change on freezing of $1.0 \ mol$ of water at $10.0^{\circ} C$ to ice at $-10.0^{\circ} C$. Given: $\Delta_{fus} H = 6.03 \ kJ \ mol^{-1}$ at $0^{\circ} C$,$C_p [H_2 O_{(l)}] = 75.3 \ J \ mol^{-1} \ K^{-1}$,$C_p [H_2 O_{(s)}] = 36.8 \ J \ mol^{-1} \ K^{-1}$.

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: