TITLE.PM5

308 ENGINEERING THERMODYNAMICS

DHARM

M-therm\Th6-1.PM5

T

Unavailable

energy

s

T 0

m

Available

energy

W= Wmax. l–m

Ql–m

l

Fig. 6.3. Unavailable energy by the second law of thermodynamics.

Thus unavailable energy is the product of the lowest temperature of heat rejection, and the

change of entropy of the system during the process of supplying heat (Fig. 6.3).

6.3. DECREASE IN AVAILABLE ENERGY WHEN HEAT IS TRANSFERRED THROUGH
A FINITE TEMPERATURE DIFFERENCE
When transfer of heat takes place through a finite temperature difference, there is a de-
crease in the availability of energy so transferred. Consider a reversible heat engine operating
between temperatures T 1 and T 0 (Fig. 6.4). Then
Q 1 = T. ∆s ;
Q 2 = T 0 ∆s ;
and W = A.E. = [T 1 – T 0 ] ∆s.

Assume that heat Q 1 is transferred through a finite temperature difference from the reser-
voir or source at T 1 to the engine absorbing heat at T 1 ′, lower than T 1 (Fig. 6.4). The availability of
Q 1 as received by the engine at T 1 ′ can be found by allowing the engine to operate reversibly in a
cycle between T 1 ′ and T 0 receiving Q 1 and rejecting Q 2 ′.
Now, Q 1 = T 1 ∆s = T 1 ′∆s′
Q T 1 > T 1 ′
∴∆s′ > ∆s
Q 2 = T 0 ∆s
Q 2 ′ = T 0 ∆s′
Q ∆s′ > ∆s
∴ Q 2 ′ > Q 2