The heats of combustion of $CH_4, C_2H_6, C_2H_4$,and $C_2H_2$ at the same temperature are $-212.8, -373.0, -337.0$,and $-310.5 \, Kcal$ respectively. Which of these gases is the best fuel?

An ideal gas undergoes a reversible isothermal expansion from state $I$ to state $II$ followed by a reversible adiabatic expansion from state $II$ to state $III$. The correct plot$(s)$ representing the changes from state $I$ to state $III$ is(are)
($p$ : pressure,$V$ : volume,$T$ : temperature,$H$ : enthalpy,$S$ : entropy)

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

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,$\Delta E = 0$.

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?
$(A)$ $T_1 = T_2$
$(B)$ $T_3 > T_1$
$(C)$ $W_{\text{isothermal}} > W_{\text{adiabatic}}$
$(D)$ $\Delta U_{\text{isothermal}} > \Delta U_{\text{adiabatic}}$

Calculate $\Delta H^{\circ}$ for the reaction, $Na_2O_{(s)} + SO_{3(g)} \longrightarrow Na_2SO_{4(s)}$, given the following reactions:
$(A) \ Na_{(s)} + H_2O_{(l)} \longrightarrow NaOH_{(s)} + \frac{1}{2}H_{2(g)} \quad \Delta H^{\circ} = -146 \ kJ$
$(B) \ Na_2SO_{4(s)} + H_2O_{(l)} \longrightarrow 2NaOH_{(s)} + SO_{3(g)} \quad \Delta H^{\circ} = +418 \ kJ$
$(C) \ 2Na_2O_{(s)} + 2H_{2(g)} \longrightarrow 4Na_{(s)} + 2H_2O_{(l)} \quad \Delta H^{\circ} = +259 \ kJ$