Modern Engineering Thermodynamics

244 CHAPTER 7: Second Law of Thermodynamics and Entropy Transport and Production Mechanisms
c. No mechanical friction occurs anywhere in the engine.
d. No chemical reactions occur anywhere in the engine.
e. No irreversibilities occur anywhere within the engine.
f. No heat transfer occurs to or from the engine.
11. a. Write either the Clausius or the Kelvin-Planck word
statements of the second law of thermodynamics.
b. Write an accurate mathematical equation for the second law.
c. Given any process, how can you determine whether it is
physically possible?
12. An inventor claims to have developed an engine that operates
on a cycle that consists of two reversible adiabatic processes
and one reversible isothermal heat addition process (see
Figure 7.24). Explain whether this engine violates either the
first or second laws of thermodynamics. (Hint: Recall that the
net work for the process is the area enclosed on the p − V
diagram.)
Pressure p
FIGURE 7.24
Problem 12.
1
Adiabatic ( 3 Q 1 = 0)
Volume V
2
Adiabatic ( 2 Q 3 = 0)
13.* If the human body is modeled as a heat engine with its
heat source at body temperature, what is its maximum
(reversible or Carnot) efficiency when the ambient temperature
is 20.0°C?
14.* An engine that operates on a reversible Carnot cycle transfers
4.00 kW of heat from a reservoir at 1000. K. Heat is then
rejected to the atmosphere at 300. K. What is the thermal
efficiency and the power output of this engine?
15. Determine whether each of the following functions could be
used to define an absolute temperature scale:
a. f (x) = cos x.
b. f (x) = tan x.
c. f (x) =x 4 .
d. f (x)=1 + x.
16.* A closed system undergoes a cycle consisting of the following
four processes:
Process 1. 10 kJ of heat are added to the system and 20 kJ of
work are done by the system.
Process 2. The system energy increases by 30 kJ adiabatically.
Process 3. 10 kJ of work are done on the system while the
system gains 50 kJ of energy.
Process 4. The system does 40 kJ of work while returning to its
initial state.
a. Complete Table 7.1 (all values in kJ).
b. Find the thermal efficiency of this cycle.
3
Table 7.1 Problem 16
Process iQ j i W j E i − E j
1
2
3
4
Totals
17.* It is proposed to heat a house using a Carnot heat pump. The
heat loss from the house is 50.0 × 10 3 J/s. The house is to be
maintained at 25.0°C while the outside air is at −10.0°C. What
coefficient of performance should the selected heat pump have,
and what minimum horsepower of the motor is required to
drive the heat pump?
18. A reversible Carnot refrigerator is to be used to remove 400. Btu/h
from a region at −60.0°F and discharge heat to the atmosphere at
40.0°F. The reversible Carnot refrigerator is to be driven by a
reversible heat engine operating between thermal reservoirs at
1040.°F and
40.0°F. How much heat must be supplied to the reversible Carnot
heat engine from the 1040.°F reservoir?
19. A reversible Carnot refrigerator is used to maintain food in a
refrigerator at 40.0°F by rejecting heat to the atmosphere at
80.0°F. The owner wishes to convert the refrigerator into a
freezer at 0.00°F with the same atmospheric temperature of
80.0°F. What percent increase in reversible work input is
required for the new freezer unit over the existing refrigerated
unit for the same quantity of heat removed?
20.* What is the cooling capacity Q L of a refrigerator with a
coefficient of performance of 3.00 that is driven by a heat
engine whose thermal efficiency is 25.0%? Both the engine and
the refrigerator are reversible, and the engine receives 600. kW of
heat energy from its high-temperature source.
21. A heat pump in a home is to serve as a heater in winter and an
air conditioner in summer. This device transfers heat from its
working fluid to air inside the house during the winter and to
air outside the house during the summer. The design conditions
(worst case) are as follows:
Winter
T house = 70.0°F
T outside = 20.0°F
_Q house = −50:0 × 10 3 Btu=h
Summer
T house = 70.0°F
T outside = 100.°F
_Q house =+30:0 × 10 3 Btu=h
Use the reversible Carnot cycle to determine the minimum
power required to drive the heat pump.
22.* The air inside a garage is to be heated using a heat pump driven by
a 500. W electric motor. The outside air is at a temperature of
−20.0°C and provides the low-temperature heat source for the heat
pump. The heat loss from the garage to the outside through the
walls and roof is 12.5 × 10 3 kJ/h. If the heat pump operates on a
reversible cycle, what is the highest temperature that can be
maintained in the garage?
23. A heat pump, with the elements shown in Figure 7.25, is to be
used to heat a home. On a given day, the evaporator receives
heat at 30.0°F and the condenser rejects heat at 70.0°F. The
required heat transfer rate from the condenser to the home is
50.0 × 10 3 Btu/h.