Modern Engineering Thermodynamics

242 CHAPTER 7: Second Law of Thermodynamics and Entropy Transport and Production Mechanisms
7. The coefficient of performance (COP) of a Carnot engine operating in reverse as a heat pump, refrigerator,
or air conditioner is
and
COP Carnot
=
heat pump
COP Carnot
=
refrig: or
air cond:
T H
T H − T L
(7.18)
T L
T H − T L
(7.20)
8. The change in specific entropy of an incompressible material (solid or liquid) with constant specific heat c is
and, for an ideal gas with constant specific heats c p and c v ,itis
ðs 2 − s 1 Þ incompressible material = c lnðT 2 /T 1 Þ (7.33)
with a constant c
ðs 2 − s 1 Þ ideal gas
= c v ln T 2
+ R ln v 2
(7.36)
T 1 v 1
constant
c p and c v
= c p ln T 2
T 1
− R ln p 2
p 1
(7.37)
9. When an ideal gas is used in an isentropic process between states 1 and 2, the following is valid:
T 2
= v 1−k
2
= p ðk−1Þ/k
2
(7.38)
T 1 v 1 p 1
10. The heat transport of entropy (S T ) Q and the heat transport rate of entropy
a constant temperature T b are
_S T across a system boundary at
Q
ðS T Þ Q
=
_q
ðτAÞ = 1 Q 2
T b act
T b act
(7.60a)
and
_S T
Q = Q _
T b act
(7.61a)
11. The work transport of entropy (S T ) W and the work transport rate of entropy _S T across a system boundary
W
are both zero:
and
ðS T Þ W = constant = 0 (7.62)
_S T
W = 0 (7.63)
12. The entropy production (S P ) Q due to an actual heat transfer inside a system of volume V during the time
interval 0 − τ is
Z Z
ðS P Þ Q
= −
V τ
_q
dT
T 2 dx
dt dV =
act
Z
V
Z
τ
σ Q dt dV (7.65)
and the entropy production rate (_S P ) Q due to an actual heat transfer inside a system of volume V is
Z
Z
_S P Q = −
V
_q
T 2
dT
dx
dV =
act
σ Q dV (7.66)
V
13. The equations for the entropy production (S P ) W due to the presence of work modes by a system depends on
the type of work mode present. For example, if the system is isothermal throughout at temperature T and an