Calculate the work done in the following reaction at $27^{\circ} C$.
$4 SO_{2(g)} + 2 O_{2(g)} \rightarrow 4 SO_{3(g)}$
$(R = 8.314 \ J \ K^{-1} \ mol^{-1})$ (in $J$)

For a spontaneous process,which of the following conditions must be met?

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 $kJ$)

For the melting of $3 \ mol$ of ice at $0^o \text{C}$,$\Delta G = \dots \dots$

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 ............ $K$.

The temperature in $K$ at which $\Delta G = 0$, for a given reaction with $\Delta H = -20.5 \ kJ \ mol^{-1}$ and $\Delta S = -50.0 \ J \ K^{-1} \ mol^{-1}$ is: