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5_60_lecture3

# 5_60_lecture3 - MIT OpenCourseWare http/ocw.mit.edu 5.60...

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MIT OpenCourseWare http://ocw.mit.edu 5.60 Thermodynamics & Kinetics Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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1 2 (2) V p p 2 p 1 V 1 5.60 Spring 2008 Lecture #3 page 1 Isothermal Gas Expansion ( T = 0) gas ( p 1 , V 1 , T ) = gas ( p 2 , V 2 , T ) Irreversibly (many ways possible) (1) Set p ext = 0 p = 0 T T p = 0 ,V p 2 2 ,V p 1 1 w (1) = − V v 1 2 p ext dV = 0 (2) Set p ext = p 2 p 2 T p 2 T ,V p 2 2 ,V p 1 1 v 2 = − p V V ( ) 2 2 1 w p dV = − V 2 - w (2) Note, work is negative: system expands against surroundings
5.60 Spring 2008 Lecture #3 page 2 (3) Carry out change in two steps gas ( p 1 , V 1 , T ) = gas ( p 3 , V 3 , T ) = gas ( p 2 , V 2 , T ) p 1 > p 3 > p 2 T p 1 1 ,V p 3 p 2 p 2 2 ,V p 3 T p 3 3 ,V T w = − p dV p dV = p V V p V V (3) V v 1 3 3 V v 3 2 2 3 ( 3 1 ) 2 ( 2 3 ) More work delivered to surroundings in this case. V 1 V 3 V 2 - w (3) p p 2 p 1 p 3 (4) Reversible change p = p ext throughout w = − V V 1 2 pdV rev Maximum work delivered to surroundings for isothermal gas V 2

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5_60_lecture3 - MIT OpenCourseWare http/ocw.mit.edu 5.60...

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