CHAPTER 3
SECOND LAW OF THERMODYNAMICS
65
Since each term has a logarithm, this equation reduces to:
or
(db3.11)
T
c
final V initial = T
c
initial V final
If ln x = ln y then ln(x/y) = 1 and x = y
For the Carnot cycle, the products are:
V A T
c
hot = V D T
c
cold
and V C T
c
cold = V B T
c
hot
(db3.12)
Dividing these two expressions gives:
V A T
c
hot = V D T
c
cold
and V C T
c
cold = V B T
c
hot
(db3.13)
Consequently, we can substitute these volume ratios into the expression for the heat flow
(eqn db3.4):
(db3.14)
V T
V T
V T
V T
A hot
c
B hot
c
D cold
c
C cold
c
=
or
V V
V
V
V
A
B
D
C
=
T
T
V
V
nal
initial
c
nal
initial
3
3
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
=
⎛
⎝
⎜
⎜
⎞
⎠ ⎠
⎟
⎟
and
or
q
T
q
T
hot
hot
cold
cold
−
=0
q
q
nRT
V
V
nRT
V
V
T
hot
cold
hot
b
a
cold
b
a
ln
ln
=
−
= −
h hot
cold
T
q
nRT
V
V
nRT
V
V
nR
cold
cold
d
c
cold
a
b
ln
ln
=
=
= − T T
V
V
cold
b
a
ln
q
nRT
V
V
hot
hot
b
a
ln
=
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