In the conversion of limestone to lime:

${{\mathrm{CaCO}}_3}_{\left(\mathrm{s}\right)} \to {\mathrm{CaO}}_{\left(\mathrm{s}\right)} +{\mathrm{CO}}_{2\left(\mathrm{g}\right)}.$

The value of $∆{\mathrm{H}}^0 \mathrm{and} ∆{\mathrm{S}}^0 \mathrm{are} 179.1 {\mathrm{kJmol}}^{-1} \mathrm{and} 160.2 {\mathrm{Jk}}^{-1}{\mathrm{mol}}^{-1}$ , respectively at $298 \mathrm{K}$ and 1bar.

Assuming $∆{\mathrm{H}}^{0 }\mathrm{and} ∆{\mathrm{S}}^0$ remain constant with temperature, at which temperature conversion of limestone

to lime will be spontaneous?