Step 3
Similar to Step 1, the work is
W 34 ¼
Z
V 4
V 3
pdV ¼ NRT B ln
V 4
V 3
Note, however, using Eq. (40) we have the relation
T A
T B
1
kÀ1 ¼
V 4
V 1
¼
V 3
V 2
It follows, therefore,
V 4
V 3
¼
V 1
V 2
and,
W 34 ¼ À
T B
T A
W 12 ¼ À
T B
T A
Q 12
Step 4
It is similarly treated as Step 2 and
W 41 ¼ Nc v T B ÀT A
ð
Þ¼ÀW 23
That is
W 41 þ W 23 ¼ 0
The NET Work performed during one cycle by the ideal gas is, thus,
W ¼ W 12 þ W 34 ¼ 1 À
T B
T A
Q 12 ¼ 1 À
T B
T A
Q A
A comparison of the expression with Eq. (45) leads to the conclusion that
T B
T A
¼
Q B
Q A
76
4 Carnot’s Theory of Heat, and Kelvin’s Adoption …
Similar to Step 1, the work is
W 34 ¼
Z
V 4
V 3
pdV ¼ NRT B ln
V 4
V 3
Note, however, using Eq. (40) we have the relation
T A
T B
1
kÀ1 ¼
V 4
V 1
¼
V 3
V 2
It follows, therefore,
V 4
V 3
¼
V 1
V 2
and,
W 34 ¼ À
T B
T A
W 12 ¼ À
T B
T A
Q 12
Step 4
It is similarly treated as Step 2 and
W 41 ¼ Nc v T B ÀT A
ð
Þ¼ÀW 23
That is
W 41 þ W 23 ¼ 0
The NET Work performed during one cycle by the ideal gas is, thus,
W ¼ W 12 þ W 34 ¼ 1 À
T B
T A
Q 12 ¼ 1 À
T B
T A
Q A
A comparison of the expression with Eq. (45) leads to the conclusion that
T B
T A
¼
Q B
Q A
76
4 Carnot’s Theory of Heat, and Kelvin’s Adoption …