Peter Atkins • Julio de Paula
Eighth Edition
Copyright © 2006 by Peter Atkins and Julio de Paula

Changes in Internal Energy at Constant Pressure
• May also express the difference in heat capacities with observables:
• C p
– C v
= nR
C
P

C
V



 
H

T 


P



 
U

T 


P
• Since H = U + PV = U + nRT
C
P

C
V



 
U

T 


P
 nR



 
H

T 


P
 nR
• And:
C
P

C
V

2
TV
T

Consider H = U + PV and H(P,T) then the full differential of H: dH




H

P


T dP




H

T


P dT
Which by rearrangement and substitution becomes: dH
 
C
P dP

C
P dT where μ ≡ the Joule-Thompson coefficient




T

P


H isenthalpic

Fig 2.27 Apparatus for measuring Joule-Thomson effect
P high
P low
• Process is adiabatic
• Gas expands through a porous barrier which acts as a throttle
• Temperature monitored to obtain ΔT
• Observed that dT
dP
• i.e.:




T

P


H

Fig 2.28 Thermo basis measuring Joule-Thomson expansion
• Process is adiabatic: q = 0, so ΔU = w w
1
= − P i
ΔV = − P i
(0 – V i
) = P i
V i w
2
= − P f
ΔV = − P f
(V f
0) = − P f
V f
So: w = w
1
+ w
2
=
P i
V i
− P f
V f
ΔU = U f
– U i
= w = P i
V i
− P f
V f
U f
+ P f
V f
= U i
+ P i
V i or: H f
= H i
∴ isenthalpic

Fig 2.30 Modern apparatus for measuring the isothermal
Joule-Thompson coefficient
P
High
T
High
P
Low
T
Low
• Measures Isothermal
Joule-Thompson coefficient




H

P


T
• Gas is pumped through a porous plug (throttle)
• Steep pressure drop is monitored on right side
• Drop in T is offset by heater
• Electrical energy
ΔH

Fig 2.29 The isothermal Joule-Thompson coefficient

• Isothermal J-T coefficient important in liquification of gases
• For real gases: μ
T
≠ 0
• If μ
T
> 0, then gas cools on expansion
• If μ
T
< 0, then gas heats on expansion at T > its inversion temperature
• Gases typically have two inversion temperatures
• One T
I at high T, the other at low T

Fig 2.31 The isothermal Joule-Thompson coefficient
• Sign of μ
T depends on conditions
T
I

Fig 2.32 The inversion temperatures for three real gases

Fig 2.33 Principle of the Linde refridgerator
T
I
Gas is recirculated
As long as its below its
T
I
, it will cool upon expansion through the throttle
Liquified gas drips from the throttle