Work Heat And First Law

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)