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45. (a) One part of path
A
represents a constant pressure process. The volume changes
from 1.0 m
3
to 4.0 m
3
while the pressure remains at 40 Pa. The work done is
33
2
(40Pa)(4.0m
1.0m ) 1.2 10 J.
A
Wp
V
=Δ=
−
= ×
(b) The other part of the path represents a constant volume process. No work is done
during this process. The total work done over the entire path is 120 J. To find the work
done over path
B
we need to know the pressure as a function of volume. Then, we can
evaluate the integral
W
=
³
p dV
. According to the graph, the pressure is a linear function
of the volume, so we may write
p
=
a
+
bV
, where
a
and
b
are constants. In order for the
pressure to be 40 Pa when the volume is 1.0 m
3
and 10 Pa when the volume is 4.00 m
3
the values of the constants must be
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 Spring '08
 Any
 Physics, Work

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