$A$ 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)

$20.0 \ dm^{3}$ of an ideal gas '$X$' at $600 \ K$ and $0.5 \ MPa$ undergoes isothermal reversible expansion until the pressure of the gas is $0.2 \ MPa$. Which of the following options is correct? (Given: $\log\,2=0.3010$ and $\log\,5=0.6989$)

If $92 \ g$ of $Na$ reacts with water in an open vessel at $300 \ K$, what is the value of work done (in $J$)? $[$Assume ideal nature of the gaseous product$]$

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

The enthalpies of combustion of cyclohexane $(C_6H_{12})$, cyclohexene $(C_6H_{10})$ and $H_2$ are $-3920 \text{ kJ mol}^{-1}$, $-3800 \text{ kJ mol}^{-1}$ and $-241 \text{ kJ mol}^{-1}$ respectively. The enthalpy of hydrogenation of cyclohexene is

State $1 \longleftarrow$ State $2 \longleftarrow$ State $3$
$\left(\begin{array}{c} T=300 \ K \\ P=15 \ bar \\ 1 \ mole \end{array}\right) \left(\begin{array}{c} T=300 \ K \\ P=10 \ bar \\ 1 \ mole \end{array}\right) \left(\begin{array}{c} T=300 \ K \\ P=5 \ bar \\ 1 \ mole \end{array}\right)$
The above shows a cyclic process. Calculate the total work done during one complete cycle. (Assume a single step to reach the next state).