Entropy Relations (Tds Equations)

ENTROPY RELATIONS (Tds EQUATIONS)

Entropy as a function of T and p:

The entropy (s) of a pure substance can be expressed as a function of temperature (T) and pressure (p).

We know that from equation (5.69),

It is known as the first form of entropy equation (or) the first Tds equation.

Entropy as a function of T and v:

By considering the entropy of a pure substance as a function of temperature (T) and specific volume (v),

From Maxwell relation,

Substituting the above expressions in ds equation,

It is known as the second form of entropy equation (or) the second Tds equation.

Entropy as a function of p and v:

As per Theorem 3 of exact differentials (Page 5.31), the entropy (s) of a pure substance can be expressed as a function of pressure (p) and specific volume (v).

i.e. s = s (p, v)

By mathematical rule,

Substituting (5.75) and (5.76) in equation (5.74),

Tds = Cp dT + Cv dT