Identify the correct statement regarding a spontaneous process.

When $2 \ mol$ of an ideal gas $\left( C_{p,m} = \frac{5}{2} R \right)$ is heated from $300 \ K$ to $600 \ K$ at constant pressure,the change in entropy of the gas $\left( \Delta S \right)$ is:

If the enthalpy of fusion of a compound at $27 \, ^\circ C$ is $2930 \, J/mol$,what is the entropy change in $J/mol \cdot K$?

Standard entropy of $X_2, Y_2$ and $XY_3$ are $60, 40$ and $50 \ J \ K^{-1} \ mol^{-1},$ respectively. For the reaction,$\frac{1}{2}X_2 + \frac{3}{2}Y_2 \to XY_3, \ \Delta H = -30 \ kJ,$ to be at equilibrium,the temperature will be ............... $K$.

One mole of an ideal gas at $350 \, K$ is in a $2.0 \, L$ vessel with thermally conducting walls,which are in contact with the surroundings. It undergoes isothermal expansion from $2.0 \, L$ to $3.0 \, L$ against a constant external pressure of $4 \, atm$. The change in entropy of the surroundings $(\Delta S_{surr})$ is $...... \, J \, K^{-1}$ (Nearest integer). Given: $R = 8.314 \, J \, K^{-1} \, mol^{-1}$.

The entropy change,in the conversion of one mole of liquid water at $373 \, K$ to vapour at the same temperature is (Latent heat of vaporization of water,$\Delta H_{vap} = 2.257 \, kJ/g$) ........ $J \, K^{-1}$ (in $.9$)