$\Delta \mathrm{H}$ and $\Delta \mathrm{S}$ for a reaction are $35.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $83.6 \mathrm{~J} \mathrm{~K}^{-1}$ respectively. Assuming that $\Delta \mathrm{H}$ and $\Delta \mathrm{S}$ do not vary with temperature, the reaction is spontaneous when:

The heat of combustion of carbon to $\mathrm{CO}_2$ is $-393.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$.

The heat released on the formation of 35.2 g of $\mathrm{CO}_2$ by combustion of C is:

Two moles of an ideal gas at 1 bar pressure and 298 K is expanded into vacuum to double the volume. The work done is :

In the decomposition of limestone to lime, the values of $\Delta H^o$ and $\Delta S^o$ are $+179.1 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $160.2 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$. Calculate the temperature above which conversion of limestone to lime will be spontaneous, if values of $\Delta H^o$ and $\Delta S^o$ remain unchanged with temperature. [Assuming pressure 1 bar ]