# Lecture 16 - Isotherms(or P-V Characteristics Recall the...

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1 Isotherms (or P-V Characteristics) Recall the definition of critical temperature: 3/2 3 (1) V Ng Instead of setting c TT , we keep T fixed and set c VV Then 3/2 3 c V (1) When there is no condensation , 3/2 3 1 () N gz V 5/2 33 3/2 5/2 3/2 1 1 1 ( ); Replace by Write v ,Then PN kT V g z kT V g z V N   5/2 3/2 v P kT No condensation c v>v When condensate starts forming cc v=v Note that v is a function of temp. 5/2 3/2 v c g P kT g (2) Substitute T from Eq.(1)   2 5/3 5/2 0 5/3 3/2 v , some constant 2 c g h Pc m g  When condensate forms c v<v , 0 3/2 3 1 NN g V (3) and 0 5/2 5/2 3 3/2 1 P N N g g kT V g    (4) Divide Eq.(3) by (1) 3/2 3 0 3/2 3 1 1 1 c c g VN V Vg 0 (5) c N

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2     5/2 3/2 (1) From 4 and 5 , c g PN kT V g 5/2 3/2 v c g kT P g , independent of v Internal Energy , Recall Canonical Ensemble ( ) N N V U nQ  Also 2 kT T     , Grand canonical ensemble zV Un Q     1 ,
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Lecture 16 - Isotherms(or P-V Characteristics Recall the...

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