Question

Explain how (without doing any calculations), given heat capacities at different temperatures, you can find the entropy change upon heating a substance.

Answer 1

Entropy is the ratio of heat transferred to the temperature in the equilibrium process.
So upon heating, we can multiply the change in temperature to the heat capacities to obtain the heat transferred at a given temperature.
The sum of the ratio of heat transferred to temperature will give the total entropy change during the heating process.
To obtain the equilibrium like heat transfer through infinte no of small steps with with infinitesimal temperature change, we integrate the ratio of heat transfer to temperature to obtain the entropy change for the given temperature change.