CHAP. 4: APPLICATION OF THERMODYNAMICS [CONTENTS] 123
4.3.5 The Joule-Thomson coefficient.
Thedifferential Joule-Thomson coefficient,μJT, is defined by the relationμJT= limp
2 →p 1T 2 −T 1
p 2 −p 1=
(
∂T
∂p)H, (4.37)
U Main unit:K Pa−^1.
It follows from relation (4.36) thatH=H(T, p) = const. From this and from equations (3.27)
and (3.28) we get
μJT=−(
∂H
∂p)( T
∂H
∂T)p. (4.38)
Substituting for the partial derivatives from (3.56) and (3.57) leads us to the relations which
are used for the calculation of the Joule-Thomson coefficient from the equations of stateμJT=T
(
∂V
∂T)p−V
Cp. (4.39)
Example
Derive the relation for the Joule-Thomson coefficient as a function of temperature and molar
volume for an ideal gas and for a gas obeying the van der Waals equation of state (2.23).