Joule-Thomson Expansion Physics 313 Professor Lee Carkner Lecture 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  ( / ) = - ( / ) 

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 = U f -U i = W + Q W = -(P f V f - P i V i ) H i = H f   For continuous throttling  h = enthalpy per mole (specific enthalpy)

Isenthalpic Curve  If a throttling process is performed, P i, T i and P f, T f can be recorded   The plot of P i, T i and all of the P f,T f ’s is called the isenthalpic curve    A series of isenthalpic curves can be produced for a substance

Inversion Curve  Each curve has two regions  T f >T i  T f < T i   = (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 c P, 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   T M.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 (P i ) 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 = (h f - h i ) / (h f - h L )  To increase amount of gas liquefied, need to decrease h i    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 