Find the approximate value of $(\Delta H - \Delta U)$ in $J \cdot mol^{-1}$,for the formation of $CO$ from its elements at $298 \ K$. $(R = 8.314 \ J \cdot K^{-1} \ mol^{-1})$

When $500 \ J$ of heat is supplied to a system at constant volume,the temperature of the system increases from $20^oC$ to $25^oC$. The change in internal energy of the system is ...... $J$.

Choose the correct option for the free expansion of an ideal gas under adiabatic conditions from the following:

One mole of an ideal gas is allowed to expand reversibly and adiabatically from a temperature of $27\, ^{\circ}C$. If the work done during the process is $3\, kJ$,then the final temperature of the gas is $(C_v = 20\, J\, K^{-1}\, mol^{-1})$ .....$K$

Two moles of an ideal monoatomic gas are allowed to expand adiabatically and reversibly from $300 \ K$ to $200 \ K$. The work done in the system is $... \ kJ$ $(C_V = 12.5 \ J/K/mol)$.

$\Delta_{vap} H^{\ominus}$ for water is $+40.49 \ kJ \ mol^{-1}$ at $1 \ bar$ and $100^{\circ} C$. The change in internal energy for this vaporization under the same conditions is . . . . . . . . . . $kJ \ mol^{-1}$. (Integer answer) (Given $R = 8.3 \ J \ K^{-1} \ mol^{-1}$)