$A$ gas absorbs $200 \ J$ of heat and expands by $500 \ cm^3$ against a constant external pressure of $2 \times 10^5 \ N \ m^{-2}$. What is the change in internal energy (in $J$)?

The law of conservation of energy states that

Assuming that water vapour is an ideal gas,the internal energy change $(\Delta U)$ when $1\, mol$ of water is vaporised at $1\, bar$ pressure and $100\, ^{\circ}C$,(given: molar enthalpy of vaporisation of water at $1\, bar$ and $373\, K = 41\, kJ\, mol^{-1}$ and $R = 8.3\, J\, mol^{-1}\, K^{-1}$) will be .............. $kJ\, mol^{-1}$

If $2 \text{ mole}$ of an ideal gas expand isothermally and reversibly at $27^{\circ}C$ from $1 \text{ dm}^3$ to $1 \text{ m}^3$, calculate the work done. [$R = 8.314 \text{ J K}^{-1} \text{mol}^{-1}$] (in $\text{ kJ}$)

$A$ gas expands isothermally against a constant external pressure of $1 \ bar$ from $10 \ dm^3$ to $20 \ dm^3$ by absorbing $800 \ J$ of heat from the surroundings. Calculate the value of $\Delta U$. (in $J$)

The $\Delta U^o$ of combustion of $CH_{4(g)}$ at a certain temperature is $-393 \ kJ/mol$. Then the value of $\Delta H^o$ is: