In conversion of lime–stone to lime, $ CaCO_3(s) \rightarrow CaO(s) + CO_2(g) $ the values of $OH ^\circ $ and $ OS ^\circ $ are $ +179.1 kJ mol ^ {–1} $ and 160.2 J/K respectively at 298 K and 1 bar. Assuming that $OH ^\circ $ and $OS ^ \circ $ do not change with temperature, temperature above which conversion of limestone to lime will be spontaneous is :
$ \triangle G ^\circ = \triangle H ^\circ – T \triangle S ^ \circ $ $ for a spontaneous process \triangle G ^ \circ \lt 0 $ $ \triangle H ^ \circ – T \triangle S ^\circ \lt 0$ $ T \triangle S ^ \circ \gt \triangle H ^ \circ $ $ T \gt { \triangle H ^ \circ \over \triangle S ^ \circ } , T \gt { 179.1 \times 1000 \over 160.2 } $ $ T \gt 1117.9 , K \approx 1118 K $ .