The property relations for
ideal gases are:
pv = RT
du = c_{v}dT
dh = c_{P}dT
The first relation of entropy change for ideal gases is obtained
by replacing P by RT/v and du by c_{v}dT in the
first Tds equation:
Tds = du + Pdv
= c_{v}dT + RTdv/v
ds = c_{v}dT/T + Rdv/v
Integrating ds from state 1 to state 2 gives the first relation of
entropy change for ideal gases.
The second relation of entropy change for ideal gases is obtained
by replacing v by RT/P and dh by c_{P}dT in the
second Tds equation:
Tds = dh  vdP
= c_{P}dT  RTdP/P
ds = c_{P}dT/T  RdP/P
Integrating ds from state 1 to state 2 gives the second relation of
entropy change for ideal gases.
A common approximation is made by assuming that the specific
heats of ideal gases are constants if the temperature variation is
small (constantspecificheats assumption). Replacing c_{v} and
c_{P} with constants c_{v,av} and c_{P,av }in
the first and second relations of entropy change and integrating from state
1 to state 2 gives,
