For a reaction to be spontaneous at any temperature,which of the following is true?

For the reaction $CaCO_{3(s)} \to CaO_{(s)} + CO_{2(g)}$,given $\Delta H^o = 178.3 \, kJ$ and $\Delta S^o = 160 \, J \cdot K^{-1}$. At what temperature will the reaction become spontaneous?

For $2 \ mol$ of $He$ (ideal gas),find the work done in a process where it is heated from $200 \ K$ to $400 \ K$ such that the enthalpy of the gas varies as : $H = 10 \ V^2$ (in $R$)

$\Delta G$ is net energy available to do useful work and is thus a measure of "free energy". Show mathematically that $\Delta G$ is a measure of free energy. Find the unit of $\Delta G$. If a reaction has positive enthalpy change and positive entropy change,under what condition will the reaction be spontaneous?

Calculate the work done when $1 \text{ mole}$ of an ideal gas is expanded reversibly and isothermally from an initial pressure $P_1 = 10 \text{ bar}$ to a final pressure $P_2 = 1 \text{ bar}$ at a constant temperature $T = 300 \text{ K}$. $[R = 8.314 \text{ J K}^{-1} \text{ mol}^{-1}]$ (in $\text{ kJ}$)

For the reaction $CaCO_3(s) \rightarrow CaO(s) + CO_2(g)$ at $298 \ K$ and $1 \ atm$ pressure,the values of $\Delta H^o$ and $\Delta S^o$ are $+179.1 \ kJ \ mol^{-1}$ and $+160.2 \ J \ K^{-1} \ mol^{-1}$ respectively. Assuming that $\Delta H^o$ and $\Delta S^o$ do not change with temperature,at what temperature (in $K$) will the process become spontaneous?