**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} = C_{P}

Therefore, (∂S / ∂T) _{P} = C_{P} X 1 / T

Hence, at constant pressure, dS = C_{P} dT / T

The substance which is perfectly crystalline, the absolute entropy S = 0 at temperature T = 0.

Therefore,

^{S}∫_{0} dS = ^{T}∫_{0} (C_{P} / T) dT

S_{T} = ^{T}∫_{0} C_{P} dT / T

S_{T} = ^{T}∫_{0} C_{P} d (ln T)

Where S_{T} is the absolute entropies of crystalline solid at constant temperature T