$36 \, mL$ 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 $... \, kJ/mol$

The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the figure. Which of the following statement$(s)$ is (are) correct?
$(A)$ $T_1 = T_2$
$(B)$ $T_3 > T_1$
$(C)$ $W_{\text{isothermal}} > W_{\text{adiabatic}}$
$(D)$ $\Delta U_{\text{isothermal}} > \Delta U_{\text{adiabatic}}$

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 $0 \ K$]

$A$ sample of argon at $1 \text{ atm}$ pressure and $300 \text{ K}$ expands reversibly and adiabatically from $1.25 \text{ dm}^3$ to $2.5 \text{ dm}^3$. Calculate the approximate enthalpy change (in $\text{J}$).
$(I)$ $C_V$ for argon is $12.48 \text{ J K}^{-1} \text{ mol}^{-1}$
$(II)$ Assume argon to be an ideal gas
$(III)$ $\Delta T = 111.5 \text{ K}$ (temperature decrease)

One mole of an ideal gas at $900 \ K$ undergoes two reversible processes,$I$ followed by $II$,as shown in the graph. If the work done by the gas in the two processes is the same,the value of $\ln \frac{V_3}{V_2}$ is. . . . . . . . ($U$: internal energy,$S$: entropy,$p$: pressure,$V$: volume,$R$: gas constant). (Given: molar heat capacity at constant volume,$C_{V, m}$ of the gas is $\frac{5}{2} R$)

Consider a reaction $2H_2O_{(l)} \to 2H_{2(g)} + O_{2(g)}$. Calculate the work done at $25\, ^oC$ for the decomposition of $36\, mL$ of water. (in $, KCal$)