Joule-Thomson Expansion

Physics 313Professor Lee

CarknerLecture 21

Exercise #20 Maxwell’s Relations Use Maxwell’s relation to find (s/P)T

(s/P)T = - (v/dT)P

P(v-b) = RT (v/dT)P = R/P

Verify relation Find s for T = 250 C and P = 200 and 400 kPa Find v for P = 300 kPa and T = 200 and 300 C (7.3789-7.7086/400-200) = - (0.8753-0.7163/300-200)

Phase Transition Processes

Some substances will easily undergo phase transitions at standard pressure

Many more materials only become liquid or solid at very low temperatures how are these temperatures achieved?

Joule-Thompson Expansion Force a fluid through a narrow plug

by maintaining unequal pressures

Can be achieved by a pump circulating fluid through a pipe with an expansion valve in the middle

Throttling and Enthalpy Apply first law:

U = Uf-Ui = W + Q

W = -(PfVf - PiVi)

Hi = Hf

For continuous throttling

h = enthalpy per mole (specific enthalpy)

Isenthalpic Curve

If a throttling process is performed, Pi, Ti and Pf, Tf can be recorded

The plot of Pi, Ti and all of the Pf,Tf’s is called the isenthalpic curve

A series of isenthalpic curves can be produced

for a substance

Inversion Curve Each curve has two regions

Tf >Ti

Tf < Ti

= (dT/dP)h

Effects of Throttling For a given initial point, the final temperature

depends on the final point on the isenthalpic curve

For > 0

For < 0

Throttling can either heat or cool a fluid

Joule-Thomson Coefficient

An expression for can be derived from dh and the second T ds equation

The slope of an isenthalpic line can

be found if you know cP, T, v and how the volume changes with temperature at that point

Liquefying Gasses In order to cool a gas, its temperature

must start below the maximum inversion temperature

TM.I. is near room temperature for many gasses

Some gasses have to be pre-cooled

Heat Exchanger How is gas liquefied?

Run at high pressure (Pi) through a heat exchanger

Cold gas runs back through the heat

exchanger cooling the incoming gas

May be pre-cooled before cycle begins

Enthalpy and Liquefaction If fraction y of the gas is liquefied and fraction

1-y is returned, what is enthalpy balance?

y = (hf - hi) / (hf - hL) To increase amount of gas liquefied, need to

decrease hi

Initial point should start on the inversion curve to maximize efficiency

TS Diagram

A TS diagram can be produced showing isobars and isenthalps

Can see that T drops most rapidly at low T and low h

Applications

Advantage is a large drop in T with P at low temperature

Often used as the last stage of a cooling process