Page 32 - Advanced thermodynamics for engineers

2.6 ENTROPY 15

2.5 THE ABSOLUTE TEMPERATURE SCALE
Carnot introduced the concept of absolute temperature from consideration of the reversible heat engine.
Kelvin realised that an absolute scale of temperature could be defined in terms of the reversible heat
engine, and would be independent of the working fluid. This must be the case, or reversible heat
engines operating between the same two temperature reservoirs with different working fluids would
have different efficiencies, which would violate the first and second corollaries.

Kelvin defined a scale such that the same quantity of work is produced by a unit fall ð1 Þ in
_
temperature irrespective of the temperature level. This means that Q=T must be constant irrespective
of the absolute temperature, T. Hence
Q _ Q _ 0 Q _ 1
¼ const ¼ ¼ ¼ etc:
T T 0 T 1
This relationship between temperature and heat flow gives the efficiency as
Q C T C T H T C
h ¼ 1 ¼ 1 ¼ (2.3)
Q H T H T H
The maximum value of efficiency is achieved when T C ¼ 0, when h ¼ 100%. An engine of this
type would be a perpetual motion machine of the second kind, denoted a PMM2. Such a device has
never been built and would violate the Kelvin–Planck statement of the Second Law.

2.6 ENTROPY
Section 2.4 shows that the ‘thermodynamic flow’ quantity to be considered in heat engines has the
_
value of Q=T. This quantity is conserved in a reversible engine; and is referred to as the ‘entropy’ flow
rate. If the heat engine is ‘irreversible’ there is a production of entropy as the energy passes through the
machine. There is no tangible analogue between this entropy production and the flow of ‘energy’ in the
hydraulic machine. A direct consequence of this is the Clausius inequality which has no counterpart in
any other field of physical science.

I
dQ
0: (2.4)
T
The significance of the inequality sign is that
I
dQ
for reversible processes ¼ 0
T
I
dQ
while; for irreversible processes < 0: (2.5)
T
Consideration of a cycle for a reversible engine leads to the conclusion that
I
dQ R
¼ 0:
T