Determine the Absolute Entropies of Solids

Absolute entropies of solids:
Entropy change for an infinitesimally small change of a state of a substance is given as:
dS = dq / T

If the changes take place at constant pressure, then,
(∂S) P = (∂q) P / T

Multiplying both the sides by ∂T, we will get:
(∂S / ∂T) P = [(∂q / ∂T) P] X 1 / T

We know that, (∂q / ∂T) P = CP
Therefore, (∂S / ∂T) P = CP X 1 / T

Hence, at constant pressure, dS = CP dT / T
The substance which is perfectly crystalline, the absolute entropy S = 0 at temperature T = 0.
Therefore,
S0 dS = T0 (CP / T) dT
ST = T0 CP dT / T
ST = T0 CP d (ln T)
Where ST is the absolute entropies of crystalline solid at constant temperature T

Category: Third Law of Thermodynamics

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