$A$ 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)

For the combustion of one mole of acetic acid,the work done at $298 \ K$ is (in $J$)

Given
$C_{(graphite)} + O_{2(g)} \rightarrow CO_{2(g)};$
$\Delta_rH^o = -393.5 \, kJ \, mol^{-1}$
$H_{2(g)} + \frac{1}{2} O_{2(g)} \rightarrow H_2O_{(l)};$
$\Delta_rH^o = -285.8 \, kJ \, mol^{-1}$
$CO_{2(g)} + 2H_2O_{(l)} \rightarrow CH_{4(g)} + 2O_{2(g)};$
$\Delta_rH^o = + 890.3 \, kJ \, mol^{-1}$
Based on the above thermochemical equations,the value of $\Delta_rH^o$ at $298 \, K$ for the reaction
$C_{(graphite)} + 2H_{2(g)} \rightarrow CH_{4(g)}$ will be ........... $kJ \, mol^{-1}$.

An ideal gas is allowed to expand both reversibly and irreversibly in an isolated system. If $T_i$ is the initial temperature and $T_f$ is the final temperature,which of the following statements is correct?

The molar heat capacity for an ideal gas at constant pressure is $20.785 \ J \ K^{-1} \ mol^{-1}$. The change in internal energy is $5000 \ J$ upon heating it from $300 \ K$ to $500 \ K$. The number of moles of the gas is [Nearest integer] (Given: $R = 8.314 \ J \ K^{-1} \ mol^{-1}$)

For which of the following processes will the value of $\Delta H^{\circ} - \Delta G^{\circ}$ be approximately zero?