Page 29 - 4461

 1   (3.9)
2

dq 2 T 2
hence 1  1 (3.10)
dq T
1 1

from last equation we can get

dq T dq 2 dq 1
2  2 , or  (3.11)
dq T T T
1 1 2 1

dq dq dq
as 2  0 , hence, we have 1  2  0 . (3.12)
T T T
2 1 2

If we take the sum of elementary processes, we get:

dq
  0 . (3.13)
T

For the reversible and irreversible processes we have:

dq
  0 (3.14)
T

Equation (54) is a mathematical expression of the Second Law of Thermodynamics for
the reversible (sign =) and irreversible (sign <) processes.
As all natural processes are irreversible, we conclude that the entropy of the
universe is always increasing. This is called the Principle of Increase of entropy. This
principle is another way of expressing the Second Law of Thermodynamics.

29