How can the entropy of a substance be derived according to standard procedures?

Calculating the entropy change of a substance from standard procedures typically involves relating it to temperature and heat capacity. The correct choice reflects a well-established thermodynamic relationship: the entropy (S) of a substance can be determined from the area under a graph of ( \frac{C_p}{T} ) against temperature (T).

This method arises from the fundamental definition of entropy in thermodynamics, where the change in entropy can be calculated using the integral:

[

\Delta S = \int \frac{C_p}{T} dT

]

In this expression, ( C_p ) represents the heat capacity at constant pressure, and ( T ) is the absolute temperature. The integral effectively sums the incremental contributions to entropy as the temperature changes. Therefore, plotting ( \frac{C_p}{T} ) against T allows for the visual determination of the total area under the curve, which corresponds to the change in entropy over the relevant temperature range.

The other choices, while related to entropy and heat capacity, do not directly utilize the entropy relationship derived from integrating ( \frac{C_p}{T} ). The area under the graph of T vs. ( C_p ) does not yield entropy directly; while heat