At $300 \ K$, $3.0 \ \text{moles}$ of an ideal gas at $3.0 \ \text{atm}$ pressure is compressed isothermally to one half of its volume by an external pressure of $6.0 \ \text{atm}$. The work done (in $kJ$) is. Given, $R=0.082 \ \text{L atm K}^{-1} \text{mol}^{-1}$ $(1 \ \text{L atm} = 101.3 \ \text{J})$.

The entropy versus temperature plot for phases $\alpha$ and $\beta$ at $1 \ bar$ pressure is given. $S_T$ and $S_0$ are entropies of the phases at temperatures $T$ and $0 \ K$,respectively.
The transition temperature for $\alpha$ to $\beta$ phase change is $600 \ K$ and $C_{p, \beta} - C_{p, \alpha} = 1 \ J \ mol^{-1} \ K^{-1}$. Assume $(C_{p, \beta} - C_{p, \alpha})$ is independent of temperature in the range of $200$ to $700 \ K$. $C_{p, \alpha}$ and $C_{p, \beta}$ are heat capacities of $\alpha$ and $\beta$ phases,respectively.
$(1)$ The value of entropy change,$S_{\beta} - S_{\alpha}$ (in $J \ mol^{-1} \ K^{-1}$),at $300 \ K$ is. . . . . . .
$(2)$ The value of enthalpy change,$H_{\beta} - H_{\alpha}$ (in $J \ mol^{-1}$),at $300 \ K$ is.
[Use : $\ln 2 = 0.69$,Given : $S_{\beta} - S_{\alpha} = 0$ at $0 \ K$]

What is the enthalpy of vaporization of ethanol in $kJ/mol$? Given: boiling point $(b.p.)$ = $79.5 \, ^\circ C$ and entropy change $(\Delta S_{vap})$ = $109.8 \, J K^{-1} mol^{-1}$.

The work done during the combustion of $9 \times 10^{-2} \ kg$ of ethane,$C_2H_{6(g)}$ at $300 \ K$ is (Given $R = 8.314 \ J \ K^{-1} \ mol^{-1}$,atomic mass $C = 12$,$H = 1$). (in $kJ$)

$A$ cylinder of gas supplied by Bharat Petroleum is assumed to contain $14 \ kg$ of butane. If a normal family requires $20,000 \ kJ$ of energy per day for cooking,how many days will the butane gas in the cylinder last? ($\Delta H_c$ of $C_4H_{10} = -2658 \ kJ/mole$)

An electric heater of power $600 \, W$ takes $8 \, \text{minutes}$ to evaporate $80 \, mL$ of water. The enthalpy of vaporization of water is ......... $kJ \, mol^{-1}$.