Formula: Entropy Change Due To Temperature Change Entropy Thermal capacity Temperature
$$\mathit{\Delta} S ~=~ C\, \mathrm{ln}\left( \frac{\class{blue}{T_2}}{\class{red}{T_1}} \right)$$
$$\mathit{\Delta} S ~=~ C\, \mathrm{ln}\left( \frac{\class{blue}{T_2}}{\class{red}{T_1}} \right)$$
$$C ~=~ \mathit{\Delta} S \, \mathrm{ln}\left( \frac{\class{red}{T_1}}{\class{blue}{T_2}} \right)$$
$$\class{red}{T_1} ~=~ \class{blue}{T_2} \, \mathrm{e}^{-\frac{\mathit{\Delta} S}{C}}$$
$$\class{blue}{T_2} ~=~ \class{red}{T_1} \, \mathrm{e}^{\frac{\mathit{\Delta} S}{C}}$$
Entropy change
$$ \mathit{\Delta} S $$ Unit $$ \frac{\mathrm J}{\mathrm K} = \frac{\mathrm{kg} \,\mathrm{m}^2}{\mathrm{s}^2 \, \mathrm{K}} $$
The entropy change \( \Delta S = S_2 - S_1 \) of an ideal gas from the initial value \(S_1\) to the final value \(S_2\).
Thermal capacity
$$ C $$ Unit $$ \frac{\mathrm J}{\mathrm K} $$
Heat capacity \( C \) is assumed here to be independent of temperature.