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Entropy Change in Ideal Gas

 



From the general property relations,'

  Tds = du + pdv 

  Tds = dh - pdv

  And for an ideal gas, du = CvdT, dh = Cp dT , and pv = RT , The entropy change between any two states   1 and 2 may be computed as given below, 

 ds = (du / T) + ( P / T ) dv 

     = Cv (dT /  T)  + R (dv / v) 

 s2 - s1 = Cv ln ( T2 - T1 )  + R ln (v2 - v1)

Also  ds = ( dh / T ) - (v / T) dp 

              = Cp (dT / T) - R ( dp / p) 

   s2 - s1 = Cp ln (T2 -T1)  - R ln (T2 -T1) 

   Since , R = Cp - Cv 

   s2  - s1 = Cp ln ( T2 -  T1 ) - Cp ln (P2 - P1) + Cv ln (P2 -P1)

   s2  - s1 = Cp ln ( v2 - v1 )  -  Cv ln (p2 / p1 ) 

The equation may be used for computing the entropy change between any two states of an ideal gas.



 




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