#3
Isothermal Gas Expansion (∆T = 0)
gas (p1, V1, T) = gas (p2, V2, T)
Irreversibly (many ways possible) (1)
Set pext = 0
p=0
T p=0 T
p 22
,V
p 11
,V
v2
w(1) =−∫V1 pextdV= 0
, 6.60 Spring 2008 Lecture page 1
(2) Set p ext = p 2
p2
p2
T T
p 22
,V
p 11
,V
v2
w (2) =−∫
V
p2dV =−p2 (VV
2 − 1)
1
p
p1
p2
V1 V2
-w(2)
Note, work is negative: system expands against surroundings
#3
(3) Carry out change in two steps gas (p1, V1, T) = gas (p3, V3,
T) = gas (p2, V2, T) p1 > p3 > p2
p2
p3
T p3 T T
p 22
,V
p 33
,V
p 11
,V
w pV p2d V=−p 3 (V 3 −V 1 )−p 2 (V V2 − 3
)
1 3
Isothermal Gas Expansion (∆T = 0)
gas (p1, V1, T) = gas (p2, V2, T)
Irreversibly (many ways possible) (1)
Set pext = 0
p=0
T p=0 T
p 22
,V
p 11
,V
v2
w(1) =−∫V1 pextdV= 0
, 6.60 Spring 2008 Lecture page 1
(2) Set p ext = p 2
p2
p2
T T
p 22
,V
p 11
,V
v2
w (2) =−∫
V
p2dV =−p2 (VV
2 − 1)
1
p
p1
p2
V1 V2
-w(2)
Note, work is negative: system expands against surroundings
#3
(3) Carry out change in two steps gas (p1, V1, T) = gas (p3, V3,
T) = gas (p2, V2, T) p1 > p3 > p2
p2
p3
T p3 T T
p 22
,V
p 33
,V
p 11
,V
w pV p2d V=−p 3 (V 3 −V 1 )−p 2 (V V2 − 3
)
1 3
