Modern Engineering Thermodynamics

Problems 245
a. If the heat pump is operated reversibly, what is the rate of
work transfer of energy to the compressor?
b. Express this compressor work rate in kilowatts and calculate
the cost per 24.0 hour day if electricity is purchased at
10.0 cents/(kW·h).
Valve
FIGURE 7.25
Problem 23.
Condenser
Evaporator
Q L
Q H
Compressor
24.* An automobile air conditioner removes 8000. kJ/h from the
vehicle’s interior. Determine the amount of engine horsepower
required to drive the air conditioner if it has a coefficient of
performance of 2.50.
25. A thermodynamic cycle using water is shown on the T-s diagram
of Figure 7.26. Calculate the coefficient of performance for this
cycle using the equation
T
FIGURE 7.26
Problem 25.
C
D
COP =
h A − h D
ðh B − h C Þ − ðh A − h D Þ
State A State B State C State D
x A = 1:00 P B = 300: psia x C = 0:00 p D = 10:0 psia
P A = 10:0 psia
The processes are
A ! B = isentropic compression,
B ! C = isobaric expansion,
C ! D = isentropic expansion,
D ! A = isothermal compression:
s
B
A
W
26.* Determine the change in total entropy of 3.00 kg of
incompressible liquid water with a specific heat of 4.20 kJ/(kg·K)
as it is heated at atmospheric pressure from 20.0°C to its boiling
point.
27. An ideal gas is compressed from 1.00 atm and 40.0°F to
3.00 atm and 540.°F. For this gas, c p = 0.280 Btu/(lbm·R) and
c v = 0.130 Btu/(lbm·R). Calculate the change in specific entropy
of this gas for this process.
28.* Determine the rate of heat transport of entropy through an
isothermal boundary at 50.0°C when the heat transfer rate at the
boundary is 350. kJ/min.
29.* Determine the heat transport of entropy into a pan of boiling
water at 100.°C that has been sitting on a kitchen stove for
30.0 min. During this time, 0.300 kg of water is converted from
a saturated liquid to a saturated vapor.
30.* If the heat entropy flux at a 2.70 m 2 boundary is given by
_q /T b = 500: × t + 243 in W/(m 2·K), where t is in seconds,
determine the total heat transport of entropy across this
boundary during the time period from t=0.00 to t=60.0 s.
31.* If the thermal entropy production rate per unit volume
is constant at 0.315 W/(m 3 · K) throughout a 0.500 m 3
system, determine the system’s rateofheatproduction
of entropy.
32. Show that the one-dimensional thermal entropy production rate
per unit volume for pure thermal conduction in a material with
a constant thermal conductivity k t is given by
σ Q = k t /T 2 ðdT/dxÞ 2 :
33. Show that the one-dimensional temperature profile inside a
system that has a constant thermal entropy production rate per
unit volume σ Q and a constant thermal conductivity k t , restricted
to pure conduction heat transfer, is given by T = T o exp½ðσ Q /k t Þ 1=2
ðx − x o ÞŠ, where T o is the temperature at x = x o .
34. If the temperature profile in Example 7.9 is given by
T = T 1 exp x L ln T
2
T 1
then
a. Show that for _Q in = _Q out the rod cannot have a constant
cross-sectional area and the areas of the ends of the rod are
related by A 2 = A 1 (T 1 /T 2 ).
b. Show that the entropy production rate under these
circumstances is given by
ð_S p Þ Q
= k tA 1
L
T1
− 1 ln T 1
T 2 T 2
c. Show that the entropy production rate of part b is greater
than that obtained with the linear temperature profile used
in Example 7.9 when A = A 1 .
35.* A stainless steel heat pipe, k 1 =30.0W/(m·K), has an isothermal
external surface temperature of 130.°C when its heat transfer rate is
1000. W. The surface area and wall thickness are 1.00 × 10 −3 m 2
and 1.00 × 10 −3 m, respectively. Determine the heat pipe’s entropy
production rate.
36.* If 0.101 grams of liquid plus vapor water at 0.0100 MPa-absolute
are put into a heat pipe 1.00 m long with an inside diameter of
5.00 × 10 −3 m, determine the temperature at which the heat pipe
phenomena cease to operate due to the complete vaporization of
the water.