TITLE.PM5

AVAILABILITY AND IRREVERSIBILITY 307

DHARM

M-therm\Th6-1.PM5

For the given values of the source temperature T 1 and
sink temperature T 2 , the reversible efficiency,
ηrev. = 1 – TT^2
1
For a given T 1 , ηrev. will increase with the decrease of
T 2. The lowest practicable temperature of heat rejection is the
temperature of the surroundings, T 0.
∴ηmax = 1 – TT^0
1

and W

T

max=−T

F

HG

I

KJ

1 0

1 Q^1

Consider a finite process l-m, in which heat is supplied

reversibly to a heat engine (Fig. 6.2). Taking an elementary

cycle, if dQ 1 is the heat received by the engine reversibly at T 1 ,

Then dW

TT

max= T

10 −

1 dQ^1

= dQ 1 – TT^0 dQ

1 1

= A.E.

Fig. 6.2. Availability of energy.

For the heat engine receiving heat for the whole process l-m, and rejecting heat at T 0

dW dQ

T

T

dQ

l

m

l

m

l

m

zzmax=−z^10

1

1

∴ Wmax = A.E. = Ql–m – T 0 (sl – sm) ...(6.1)

or unavailable energy, U.E. = Ql–m – Wmax

or U.E. = T 0 (sl – sm)

Fig. 6.1. Available and unavailable

energy in a cycle.