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Entropy Change of an Ideal Gas

From equation (9.3) we have

ds = du / t + pu /t

= cu dt / t + R du / u

Entropy change between state 1-2

or                                        s2 – s1 = c2 In T2 / T1 + R In v2 /v1

we also have                          Tds = dh  udp

ds = dh / T– udp /T

= cp dt / t – R dp /p

 

Entropy change between two states 1 – 2 can also be written as

s2 – s1 = cp In T2 / T1 –R In P2 / P1

As                               cp – cu = R, equation (9 .19) can be written as

s2 – s1 = cp In T2 / T1 – cp In P2 P1 + c2 In P2 / P1

or                                 s2 –s1 = cp In P1 T1 / P2 T2 + c2 In P2 / P1

or                                 s2 – s1 = cp In v2 / v1 + c2 In p2 / p1

or                                 s2 – s1 = cp In v2 / v1 + cv In p2 / p1

 

We can use equations (9.18), (9.19), (9.20) for computing the e::1tropy change between

two states of an ideal gas.