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Work Heat And First Law
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Notes for Work heat and first law by Jatin Sharma
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Work, Heat, and the First Law• Work: w =F ⋅
applied force distance
Expansion work
F =pextA w = −
(pextA) = −pext ∆V
convention: Having a “-“ sign here implies w > 0 if ∆V < 0 , that
is, positive work means that the surroundings do
work to the system. If the system does work on the
surroundings (∆V > 0) then w < 0.
-
If pext is not constant, then we have to look at infinitesimal changes d
-
w =−pextdV d means this is not an exact differential Integral w
=−
∫ pextdV
1
2
depends on the path!!!
• Path dependence of w
Example: assume a reversible process so that pext = p
Ar (g, p1, V1) = Ar (g, p2, V2)
, 5.60 Spring 2008 Lecture #2 page 1
Compression V1 > V2 and p1 < p2
p ext= p 1
p ext= p 2
p 11
,V co m pression
p 22
,V
initial final
Two paths:
(1) First V1 → V2 at p = p1 then p1 → (2) First p1 → p2 at V = V1 then
p2 at V = V2 V1 → V2 at p = p2
Ar(g, p1, V1) = Ar(g, p1, V2) = Ar(g, p2, V2) Ar(g, p1, V1) = Ar(g, p2, V1) = Ar(g, p2, V2)
p
p2
final 1
(2)
p1 init.
(1)
V2 V1
V1 V2
w (1) pext dV ∫V pext dV w (2 ) =−∫V pext dV ∫V pext dV
V2
− −
2 1 1
p1dV p2dV = −p2 (V V 2 − 1 )
w (1) =p 1 w (2) =p 2 (V V1
− − 2 )
(Note w > 0, work done to system to compress it)
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