State the limitation of the $2^{nd}$ law of thermodynamics.

One mole of an ideal diatomic gas $(C_V = 5 \ cal)$ was transformed from initial $25 \ ^{\circ}C$ and $1 \ L$ to the state when temperature is $100 \ ^{\circ}C$ and volume $10 \ L$. The entropy change of the process can be expressed as $(R = 2 \ cal / mol \cdot K)$ :-

The enthalpy of fusion of water is $6.01 \, kJ \, mol^{-1}$. The entropy change of $1 \, mole$ of ice at its melting point will be.....$J \, K^{-1} \, mol^{-1}$.

For the vaporization of water at $1 \, \text{atm}$ pressure,the liquid water and water vapor are in equilibrium. What is the temperature in $K$?
$H_2O_{(l)} \rightleftharpoons H_2O_{(g)}$ [at $1 \, \text{atm}$ pressure] [$\Delta S = 120 \, J K^{-1}$ and $\Delta H = +45.0 \, kJ$]

The $S^o$ of the following substances are:
$CH_{4(g)} : 186.2 \ J \ K^{-1} \ mol^{-1}$
$O_{2(g)} : 205.2 \ J \ K^{-1} \ mol^{-1}$
$CO_{2(g)} : 213.6 \ J \ K^{-1} \ mol^{-1}$
$H_2O_{(l)} : 69.9 \ J \ K^{-1} \ mol^{-1}$
The entropy change $\Delta S^o$ . . . . . . $J \ K^{-1} \ mol^{-1}$ for the reaction
$CH_{4(g)} + 2O_{2(g)} \to CO_{2(g)} + 2H_2O_{(l)}$ is

Identify the correct statement regarding a spontaneous process: