Modern Engineering Thermodynamics

Summary 203
59. Incompressible liquid water—density = 62.4 lbm/ft 3 and specific
heat=1.00Btu/(lbm· R)—at 70.0°F is pumped into a rigid
insulated hollow bowling ball. Determine the temperature of the
water in the bowling ball when its pressure reaches 100. × 10 3 psia.
60.* A 0.100 m 3 rigid tank is filled adiabatically to 20.0 MPa with
helium. If the helium enters the tank at 20.0°C, determine the
final temperature in the tank after it is filled. Assume ideal gas
behavior with constant specific heats.
61.* Determine the heat transfer required to fill an initially empty
rigid vessel isothermally with 15.0 kg of pure oxygen at 20.0°C.
Assume ideal gas behavior with constant specific heats.
62. Determine the heat transfer required to cause a tank initially
pressurized with air to discharge isenthalpically. The initial state
inside the tank is p 1 = 1500. psia, T 1 =100. o F, m 1 = 10.0 lbm and
the final state is p 2 =14.7psiaandm 2 = 0.098 lbm. Assume
ideal gas behavior.
63.* A rigid tank with a volume of 0.500 m 3 contains superheated steam
at 40.0 MPa and 500.°C. A valve on the tank is suddenly opened
and steam is allowed to escape until the pressure in the tank is
1.00 MPa. While the steam is escaping, heat is simultaneously
added to the tank in a manner that causes the specific enthalpy
inside the tank to remain constant throughout the emptying
process. Determine the total heat transfer required for this process.
64. Consider a rigid tank of volume V:
a. Show that the heat transfer rate required to empty or fill the
tank isenthalpically (note that you must show that this is
true for both cases) is given by
_Q isenthalpic
empty or fill
= −Vðdp/dtÞ
b. Then show that the total heat transfer required to carry out
this isenthalpic process from state 1 to state 2 is given by
ð1Q 2 Þ isenthalpic
empty or fill
Computer Problems
= Vp ð 1 − p 2 Þ
The following computer problems were designed to be completed
using a spreadsheet or equation solver. They may be used as part of a
weekly homework assignment.
65. Develop a computer program that calculates the output velocity
of an incompressible fluid flowing through an adiabatic nozzle.
Input all the necessary variables with the proper units.
66. Develop a computer program that calculates the output pressure
of an incompressible fluid from an adiabatic diffuser. Input the
necessary variables with the proper units.
67. Develop a computer program that calculates the temperature of
one of the four flow streams of a heat exchanger having two
inlets and two outlets, when the mass flow rates and fluid
properties of both of the flow stream fluids are known. Assume
the fluids do not mix inside the heat exchanger and have one
flow stream be an incompressible liquid and the other a
constant specific heat ideal gas. Input the necessary variables
with the proper units.
68. Develop a computer program that performs an energy rate
balance on a gas turbine engine. Input the appropriate gas
properties (in the proper units), the turbine’s heatlossorgain
rate, and the input mass flow rate, and inlet and exit
temperatures. Output the turbine’s output power. Assume the
gas behaves as a constant specific heat ideal gas and neglect all
kinetic and potential energy terms.
69. Develop a computer program that performs a steady state energy
rate balance on an open system containing an ideal gas with
constant specific heats. Input all but one (you choose which
one) of the following quantities (in proper units): the heat and
work energy transport rates, the mass flow rate, temperature,
velocity and height of each flow stream entering and exiting the
system, and the constant pressure specific heat of the gas
contained in the system. Calculate the specific enthalpy of the
gas using h = c p T, where T is in absolute temperature units. One
of these items is not supplied by the user and therefore becomes
the unknown to be determined by the program. Output all the
input variables plus the value of the unknown.
70. Repeat Problem 69, except use an incompressible liquid as the
working fluid. Allow the user of your program to choose which
variable is to be the unknown from a screen menu, then prompt
for all the remaining variables. Use the conservation of mass law
to determine or check the balance of the mass flows.
Create and Solve Problems
Engineering education tends to focus only on the process of solving
problems. It ignores teaching the process of formulating solvable
problems. However, working engineers are never given a well-phrased
problem statement to solve. Instead, they need to react to situational
information and organize it into a structure that can then be solved
using the methods learned in college.
These “Create and Solve” problems are designed to help you learn
how to formulate solvable thermodynamics problems from engineering
data. Since you provide the numerical values for some of the variables,
these problems do not have unique solutions. Their solutions
depend on the assumptions you need to make and how you set
them up to create a solvable problem.
71.* A canned pickle manufacturer wants to carry out the canning
and sterilization process at 100. kPa. You have a 1.50. MPa
steam line available at the sterilizer, containing steam with
5.00% moisture. You decide to drop the pressure from 250. to
100. kPa through a throttling orifice. Write and solve a
thermodynamics problem that determines the 100. kPa (a) at
exit temperature and (b) the exit quality.
72.* A design for a pump has been proposed involving the
adiabatic, steady flow of liquid water through the pump.
Saturated liquid water at 180.°C enters the pump and
compressed water leaves at 2.20 MPa. Your section chief
wants to know the work per unit mass of water flowing
through the pump. Write and solve a thermodynamics
problem that provides her with the answer.
73. Your boss comes to you with a new design for an insulated
domestic electric water heater that is supposed to heat 1.00
gallons per minute of water from 50.0ºF to 140.ºF, but the
outlet temperature reaches only 105ºF. Your boss wants you to
determine how much electrical power is needed to meet the
design specifications. Write and solve a thermodynamics
problem that provides him with the answer.