linguistic:paraphrasing
Cooling and heating

For pure heating or cooling of any system (gas, liquid or solid) at constant pressure from an initial temperature T 0 {\textstyle T_{0}} to a final temperature T {\textstyle T}, the entropy change is:

provided that the constant-pressure molar heat capacity (or specific heat) C P {\textstyle C_{\mathrm {P} }} is constant and that no phase transition occurs in this temperature interval.

Similarly at constant volume, the entropy change is: Δ S = n C V ln T T 0 {\displaystyle \Delta S=nC_{\mathrm {V} }\ln {\frac {T}{T_{0}}}} where the constant-volume molar heat capacity C V {\textstyle C_{\mathrm {V} }} is constant and there is no phase change.

At low temperatures near absolute zero, heat capacities of solids quickly drop off to near zero, so the assumption of constant heat capacity does not apply.

Since entropy is a state function, the entropy change of any process in which temperature and volume both vary is the same as for a path divided into two steps – heating at constant volume and expansion at constant temperature. For an ideal gas, the total entropy change is: Δ S = n C V ln T T 0 + n R ln V V 0 {\displaystyle \Delta S=nC_{\mathrm {V} }\ln {\frac {T}{T_{0}}}+nR\ln {\frac {V}{V_{0}}}} Similarly if the temperature and pressure of an ideal gas both vary: Δ S = n C P ln T T 0 − n R ln P P 0 {\displaystyle \Delta S=nC_{\mathrm {P} }\ln {\frac {T}{T_{0}}}-nR\ln {\frac {P}{P_{0}}}}