One of the beauties of thermodynamics is that it provides interrelationships between various state variables and their

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One of the beauties of thermodynamics is that it provides interrelationships between various state variables and their derivatives so that information from one set of experiments can be used to predict the results of a completely different experiment. This is illustrated here. 

a. Show that

CP || T (0(V/T) ( rl T P

Thus, if the Joule-Thomson coefficient μ and the volumetric equation of state (in analytic or tabular form) are known for a fluid, CP can be computed. Alternatively, if CP and μ are known, (∂(V /T)/∂T)P can be calculated, or if CP and (∂(V /T)/∂T)P are known, μ can be calculated. b. Show that

P,T T2 Cp 5) = 2/X (P.T.) +1 [10  T Sp -V(P, T) dT T P,T1 V(P, T)=

so that if μ and CP are known functions of temperature at pressure P, and V is known at P and T1, the specific volume at P and T2 can be computed. 

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