Page 31 - Advanced thermodynamics for engineers

14 CHAPTER 2 THE SECOND LAW AND EQUILIBRIUM

The other statement of the Second Law, attributed to Clausius, states
It is impossible to construct a system which will operate in a cycle and transfer heat from a cooler to
a hotter body without work being done on the system by the surroundings.
It is possible to derive six corollaries of the Second Law, and these will simply be stated here.
Corollary 1
It is impossible to construct a heat engine to work between two heat reservoirs which has an
efficiency which exceeds that of a reversible engine operating between the same two reservoirs.
Corollary 2
All reversible heat engines operating between the same two heat reservoirs have the same thermal
efficiency.
Corollary 3
A temperature scale may be defined which is independent of the thermometric substance.
Corollary 4
This is often referred to as the Clausius inequality and defines a relationship for the net heat transfer
of a cyclic process.
Whenever a system executes a complete cyclic process (i.e. a cycle) H dQ 0
cycle T
Corollary 5
This corollary defines the property entropy, which is the property associated with the Second Law
of thermodynamics. Entropy is a measure of the transformation brought about by a process and is
also an indicator of the direction of a process.
H R
dQ R dQ R
¼ 0 for any reversible, cyclic process. Hence, is a property of any reversible process
cycle T T
between a reference state 0 and any other state 1. This property is called entropy.
Corollary 6
This is an important concept which shows that the degree of disorder in the universe will increase.
If there is an increase in the order of a part of the universe, then it is accompanied by a decrease in
the order of the remainder of the universe.
The entropy of an isolated system increases, or in the limit remains constant.

2.4 THE CONCEPT OF THE HEAT ENGINE: DERIVED BY ANALOGY WITH A
HYDRAULIC DEVICE (TABLE 2.1)

Table 2.1 A Comparison of Parameters Defining Power Output and Efficiency for Engines
Hydraulic Machine Thermodynamic Machine
‘Forcing’ quantity Head of water (h 1 h 2 ) Temperature difference (T 1 T 2 )
‘Flowing’ quantity Weight flow rate _ mg Entropy flow rate _ s ¼ _ Q=T
Work output rate _ mgðh 1 h 2 Þ _ sðT 1 T 2 Þ
Efficiency h ¼ h 1 h 2 h ¼ T 1 T 2
h 1 T 1