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

What is the work done when $1 \, \text{mole}$ of a gas expands isothermally and reversibly from $25 \, \text{L}$ to $250 \, \text{L}$ at a temperature of $300 \, \text{K}$? (in $J$)

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) $(R=8.3 \ J \ K^{-1} \ mol^{-1})$

For the reaction $C_{(graphite)} + CO_{2(g)} \rightarrow 2CO_{(g)}$,$\Delta H = 170 \ kJ$ and $\Delta S = 170 \ J/K$. At what temperature $(K)$ will the reaction become spontaneous?

$\Delta G$ 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?

The values of $\Delta H$ and $\Delta S$ of a certain reaction are $-400 \text{ kJ mol}^{-1}$ and $-20 \text{ kJ mol}^{-1} \text{ K}^{-1}$ respectively. The temperature below which the reaction is spontaneous,is