Heat and Thermodynamics

7.3 Calculation of Amount of Cooling

In a throttling process,

 

dH = 0

     TdS = du + p dv

 

or

 

     du = T dS − p dv

 

Now

     du + d (pv) = T dS − p dv + d (p v)

     = T dS − p dv + p dv + v dp

     d(u + pv) = T dS + v dp

 

or

 

     dH = T dS + v dp

 

or

 

T dS + v dp = 0       (7.4)

 

Expressing S as a function of p and T,

 

 

Substituting the value of dS in Eq. 7.4, we get

 

 

Using fourth Maxwellian relation, Eq. 7.5 becomes

 

 

so that

 

 

or

 

 

or

 

 

The quantity (dT/dp)_H is called the cooling coefficient produced ...