# Entropy Change of an Ideal Gas

Original equation for entropy change:

First of all we will consider ds = du / t + pu /t

= cu dt / t + R du / u from equation of 9.3 and then coming to Entropy change between state 1 – 2 :

= 2ʃ1 ds = 2ʃ1 cvdT/ T + 2ʃ1 R dv/v

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

we also have                          Tds = dh  udp

ds = dh / T– udp /T

= cpdt / t – R dp /p

Equivalent equations for entropy change:

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

Also, s2 – s1 = cp, in v2 / v1 + c2In 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 betweentwo states of an ideal gas.

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