For a reaction to be spontaneous at all temperatures,which of the following conditions must be satisfied?

Calculate the work done in Joules $(J)$ when $50 \ g$ of iron is dissolved in $HCl$ in an open beaker at $25 \ ^oC$. The atmospheric pressure is $1 \ atm$.

In the conversion of limestone to lime,$CaCO_{3(s)} \rightarrow CaO_{(s)} + CO_{2(g)}$,the values of $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are $+179.1 \ kJ \ mol^{-1}$ and $160.2 \ J \ K^{-1} \ mol^{-1}$ respectively at $298 \ K$ and $1 \ bar$. Assuming that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ do not change with temperature,the temperature above which the conversion of limestone to lime will be spontaneous is ........... $K$.

For the reaction $Ag_2O_{(s)} \rightarrow 2Ag_{(s)} + 1/2 O_{2_{(g)}}$,the value of $\Delta H = 30.56 \, kJ \, mol^{-1}$ and $\Delta S = 66 \, J \, K^{-1} \, mol^{-1}$. At what temperature $(K)$ will the change in free energy for the reaction be zero?

At $273 \ K$ the maximum work done when pressure on $10 \ g$ of hydrogen is reduced from $10 \ atm$ to $1 \ atm$ under isothermal,reversible conditions is (Assume the gas behaves ideally) $(R=8.3 \ J \ K^{-1} \ mol^{-1})$

Gibbs free energy $G$,enthalpy $H$ and entropy $S$ are interrelated as in