Modern Engineering Thermodynamics

274 CHAPTER 8: Second Law Closed System Applications
However, most systems of engineering interest do not undergo reversible processes, and the entropy produced
by the irreversiblilties inherent in the system is of great value in the design process. Both the direct method and
the indirect method can be used to find values for the entropy produced in any irreversible process. The indirect
method is used in several examples developed in this chapter to determine the entropy produced by heating a
fluid in a simple closed container, a lightbulb, a food blender, a typical electrical power plant, and so forth. The
more complex direct method is then used to determine the entropy produced by convective heat transfer from a
cooling fin, the viscosity of the lubricant liquid in an engine bearing, the electrical resistance of a circuit board,
and the diffusional mixing of identical fluids.
Problems (* indicate problems in SI units)
1.* Air contained in a cylinder fitted with a piston initially at
2.00 MPa and 2000.°C expands to 0.200 MPa in an isentropic
process. Assuming the air behaves as a constant specific heat
ideal gas, determine the following:
a. The final temperature.
b. The change in specific internal energy.
c. The change in specific enthalpy.
d. The change in specific entropy.
e. The work done per lbm of air during the expansion.
2. A constant specific heat ideal gas has a gas constant of 42.92 ft ·
lbf/(lbm· R) and a constant pressure specific heat of 0.200Btu/
(lbm· R). Determine the heat transferred and the change of total
entropy if 9.00 lbm of this gas is heated from 40.0°F to 340.°F
in a rigid container.
3. A reversible Carnot heat engine has 1.00 lbm of air as the
working fluid. Heat is received at 740.°F and rejected at 40.0°F.
At the beginning of the heat addition process, the pressure is
100. psia and during this process the volume triples. Calculate
the net cycle work per lbm of air. Assume the air behaves as a
constant specific heat ideal gas.
4. A 1.000 ft 3 glass bottle is initially evacuated then has 1.000 g of
water added that eventually comes to equilibrium at 70.00°F. The
pressure in the bottle is increased by 11.1668 psia during a
reversible adiabatic compression:
a. What is the work done during compression?
b. What is the entropy production for the compression?
5. 3.00 lbm of Refrigerant-134a (not an ideal gas) is compressed
adiabatically in a closed piston-cylinder device from 5.00 psia,
220.°F to 200. psia, 340.°F.
a. Determine the work for this process.
b. Show whether or not this process violates the second law of
thermodynamics.
6.* An engineer claims to be able to compress 0.100 kg of water
vapor at 200.°C and 0.100 MPa in a piston-cylinder
arrangement in an isothermal and adiabatic process. The
engineer claims that the final volume is 6.10% of the initial
volume. Determine
a. The final temperature and pressure.
b. The work required.
c. Show whether the process is thermodynamically possible.
7. An inventive engineer claims to have designed a
mechanochemical, single-stroke closed system that compresses
l0.0 lbm of air isothermally from 14.7 psia, 100.°F to 200. psia
while inputting 500. Btu of mechanochemical compression
work. Assuming constant specific heat ideal gas behavior,
a. What heat transfer is required for this process to occur?
b. Does this process violate the second law of thermodynamics?
8.* Saturated liquid water at 8.58 MPa undergoes a reversible
isothermal process in a cylinder until the pressure reaches
0.100 MPa. Calculate the heat transfer and work per kg of water
for this process. Show the process on a T-s diagram. Neglect any
changes in kinetic and potential energies.
9.* Air is compressed in a steady state reversible adiabatic process
from 25.0°C and 0.150 MPa to 1.70 MPa. Determine the change
of specific enthalpy in this process and find the density of the exit
air. Assume the air behaves as an ideal gas with constant specific
heats. Neglect any changes in kinetic and potential energies.
10.* One cubic meter of hydrogen (a constant specific heat ideal gas)
expands from an initial pressure of 0.500 MPa to a final
pressure of 0.100 MPa. The gas temperature before expansion
is 27.0°C.
a. Determine the final temperature if the process is isentropic.
b. Determine the final temperature if the process is polytropic
with n=1.30.
c. Calculate the heat transfer required for the polytropic case.
11. 2.00 lbm of saturated water vapor at 247.1 psia undergoes a
reversible isothermal expansion until the pressure reaches
20.0 psia. Determine the heat transfer and the work done for
this process. The system boundary temperature is the same as
the process temperature.
12. Consider a fixed mass of a constant specific heat ideal gas in a
piston-cylinder device undergoing a compression process for
which pV n = constant (a polytropic process). Show that the
work done per unit mass of gas in such a process is given by
(p 2 v 2 – p 1 v 1 )/(n – 1) if n ≠ 1. If the process is isentropic, show
that this reduces to c v (T 2 – T 1 ).
13.* 0.130 kg of a constant specific heat ideal gas is compressed in a
closed system from 1.00 atm and 40.0°C to 11.39 atm in an
isothermal process. For this gas, c p = 523 J/(kg·K), c v = 315 J/
(kg·K), and R = 208 J/(kg·K). For this process, determine
a. The work required.
b. The resulting heat transfer.
c. The amount of entropy produced.
d. Explain whether this process violates the second law of
thermodynamics.
14. Show that a constant specific heat ideal gas undergoing a
constant heat flux polytropic process (pv n = constant with n ≠ 1)
has a limiting isothermal system boundary temperature
corresponding to a reversible process given by
ðT b Þ rev
= T 2 − T 1
lnðT 2 /T 1 Þ
(Hint: Recall that 1 W 2 =mR(T 2 – T 1 )/(n – 1) for such a
polytropic process with an ideal gas.)