For the $1^{st}$ law of thermodynamics,select the correct option.

When $100 \ cal$ of heat is supplied to a system,the work done by the system is $300 \ J$. The change in internal energy of the system is ..... $J$.

The relation between $\Delta H$ and $\Delta U$ for the reaction $2 SO_{3(g)} \longrightarrow 2 SO_{2(g)} + O_{2(g)}$ is:

The enthalpy of vaporization of water at $100 \, ^\circ C$ is $40.63 \, kJ \, mol^{-1}$. The value of $\Delta U$ for this process is ....... $kJ \, mol^{-1}$.

The first law of thermodynamics for an isothermal process is:

For water $\Delta_{vap} H = 41 \ kJ \ mol^{-1}$ at $373 \ K$ and $1 \ bar$ pressure. Assuming that water vapour is an ideal gas that occupies a much larger volume than liquid water,the internal energy change during evaporation of water is $...... \ kJ \ mol^{-1}$.
[Use: $R = 8.3 \ J \ mol^{-1} \ K^{-1}$]