TITLE.PM5

SECOND LAW OF THERMODYNAMICS AND ENTROPY 233

dharm

/M-therm/th5-1.pm5

reverse the engine and for the reversible heat pump obtained it is possible to develop the

expression,

− F

HG

I

KJ

∑ δQ ≤

cycle T

0

The negative sign indicates that the heat transfers have all reversed in direction when the

engine was reversed. This means that for the same machine we have two relations which are only

satisfied if in the reversible case,

δQ

T

F

HG

I

KJ

∑ ≤

cycle

(^0) ...(5.13)
For a reversible case, as the number of reservoirs used tends to infinity, the limiting value
of the summation will be
δQ
T
F
HG
I
KJ
∑ =
cycle
0
In words, the Clausius inequality may be expressed as follows :
“When a system performs a reversible cycle, then
δQ
T
F
HG
I
cycle∑ KJ = 0,
but when the cycle is not reversible
δQ
T
F
HG
I
KJ
∑ <
cycle
0 ’’.

5.8. Carnot Cycle

The cycle was first suggested by a French engineer Sadi Carnot in 1824 which works on
reversible cycle and is known as Carnot cycle.
Any fluid may be used to operate the Carnot cycle (Fig. 5.5) which is performed in an engine
cylinder the head of which is supposed alternatively to be perfect conductor or a perfect insulator of
a heat. Heat is caused to flow into the cylinder by the application of high temperature energy
source to the cylinder head during expansion, and to flow from the cylinder by the application of a
lower temperature energy source to the head during compression.

Heat source

at T 1

Sink at T 2

Piston

Cylinder

(a)