Calculate the work done if $1 \ mole$ of a certain gas is compressed isothermally and reversibly at $300 \ K$ from an initial pressure $x \ bar$ to a final pressure $2x \ bar$ $[R = 8.314 \ J \ K^{-1} \ mol^{-1}]$. (in $kJ$)

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 $J$)

For a spontaneous change,free energy change $\Delta G$ is

$\Delta G$ 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 $\Delta S$ for the reaction,$C_{(graphite)} + CO_{2(g)} \rightarrow 2CO_{(g)}$ are $170 \ kJ$ and $170 \ J \ K^{-1}$ respectively. This reaction will be spontaneous at temperatures greater than ............ $K$.

Calculate the work done during the reversible isothermal expansion of $2 \ mol$ of an ideal gas at $298 \ K$ from $10 \ L$ to $20 \ L$ in $J$. (in $.9$)