SOLUTIONS
THERMODYNAMICS PRACTICE PROBLEMS FOR NON-TECHNICAL MAJORS
Thermodynamic Properties
1. If an object has a weight of 10 lbf on the moon, what would the same
object weigh on Jupiter?
gJupiter = ft ft lbm-ft
gMoon = gc =
75 sec2 sec2 lbf-sec2
5.4 32
––K mg –– 10×32
W m= K g = = 59.26 lbm
= W moon
c
gc gmoon 5.4
––K mgJupiter 59.26×75
W = = = 139 lbf
Jupiter gc 32
2. An object that weighs 50 lbf on earth is moved to Saturn where its new weight
is 105 lbf. What is the acceleration due to gravity on Saturn?
gEarth = ft lbm-ft
gc =
32 sec2 lbf-sec2
32
50 lbf onearth 50 lbm
––K
––K mg W 105 32 ft
gc 67.2
W= g sec2
gc m 50
3. Define, using equations, specific volume (ν) and density (ρ) . What is the
mathematical relationship between these two terms?
V m 1 1
, , or
m V
Temperature and Pressure Measurements
4. (a) Define temperature.
(b) What is the absolute temperature scale corresponding to Fahrenheit?
(c) Convert 100 F to that absolute scale.
(a) Temperature: a measure of molecular activity of a substance.
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(b) Rankine
(c) R = F + 460 100 F converts to 560 R
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5. Define pressure.
Pressure: a measure of force exerted per unit area on the boundaries of a
system.
6. If PA=PB, in which direction will the piston move? Explain, using equations.
A B
F
P=
A
A A F F F F
P=
B A B A
A
Piston will move to the left.
7. Given: P1 = 4 psig, PATM = 15 psia, and P2 = 10 psig
Find PA and PB.
ATM
Pgage = P
system - Preference
P1 = PATM - PB 11 psia
= 15 psia - 4 psia =
PB
21 psia
P2 =
- = 10 psig + 11 psia =
PA PB PA
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8. Given: PATM = 15 psia, P2 =6 psiv, and P3 = 7
psig Find PA and PB.
ATM
Pgage = P
system - Preference
P3 = 22 psia
- PATM = 15 psia + 7 psia =
PA
PA
28 psia
P2 =
-P = 22 psia - (- 6) psi =
PA B PB
9. Given the conversion factor 1 inch H2O = 0.0361 psid and that the manometer
below employs water, find the difference in pressure between compartments A
and B.
A B
6 ft
∆P = 6 ft 12
0.0361psid
in 1in =
2.6 psid
1ft
Energy, Work, and Heat
10. Define energy.
Energy: the capacity of a system to perform work or produce heat.
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11. Define, using equations, the total kinetic energy, total potential energy,
and enthalpy.
mgz
PE
gc
mv 2
KE
2gc
h u P
12. Given the following information about a system, calculate specific enthalpy (in
Btu/lbm).
ft3 Btu
P=100 psia =1.6 u = 600 Note: 778 ft-lbf=1
Btu lbm lbm
h u P
Btu lbf ft 3 Btu
h 600 (100 2 )(1.6 )(144 in )( ) 629.6 Btu
lbm in lbm 2 778 ft lbf lbm
ft 2
13. Given the following information about a system, calculate specific internal energy
(in Btu/lbm).
ft3 Btu
P=200psia =2.8 h=1000 Note:778 ft-lbf=1Btu
lbm lbm
h u P u h P
Btu lbf ft 3 144 in Btu Btu
u 1000 (200 2
)(2.8 )( 2 )( ) 896.3
lbm in lbm 778 ft lbf lbm
ft 2
14. A 5 lbm system was taken from 50 F to 150 F. How much energy in the form of
heat was added to the system to produce this temperature increase?
cp =1.6 Btu
lbm-F
Q mcp (Thot Tcold )
Q 5lbm1.6 Btu 800Btu
(150 50)F
lbm F
15. A 10 lbm metal ball has a temperature of 200 F when it is placed in a 50 lbm
bath of water at room temperature (72 F). Heat transfer occurs between the two
substances until equilibrium is reached. Find this equilibrium temperature.
c =1.0 Btu Btu
p
Water c =
lbm-F 4.3 lbm-F
p Metal
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QOut QInWater
Ball
mballcball (Tball Teq ) mwater cwater (Teq Twater )
initial initial
(mcT )ball (mcT )water
Teq (mc) (mc)
ball water
10 lbm 4.3 Btu 200 F 50 lbm 1.0 Btu 72 F
lbm F
lbm F
Teq
50 lbm 1.0Btu 10 lbm 4.3
lbm F Btu
Teq 131.2F lbm F
16. During a phase change, the specific entropy of a 20 lbm system increases from
0.31 Btu Btu
to 1.61 while the temperature of the substance is a constant
lbm lbm
R R
212F.
Find the heat transfer into this system.
Hint: Must convert temperature to Rankine.
20
Q m T s 212 460 1.61 0.31 Btu
lbm R lbm R 17, 472 Btu
17. A nuclear power plant is found to generate 80 MW of power. A typical Honda
civic is capable of producing 150 HP. How many Honda Civic’s would be
required to generate the equivalent power of this nuclear power plant?
Use the energy and power equivalences found in the DOE Fundamentals
Handbook (see Pages 23 and 24 of the “Energy, Work, and Heat” module).
80 MW 1000 KW 3, 413BTU 1HP hr 1Honda Civic
715.23 716 Honda Civics
1MW 1KW hr 2, 545 BTU 150 HP
Thermodynamic Systems and Processes
18. Define isolated system, closed system, and open system.
Isolated system – A system that is not influenced in any way by its surroundings
(mass and energy do not cross the system boundary).
Closed System – A system which has no transfer of mass with its surroundings,
but that may have a transfer of energy.
Open System – A system that may have a transfer of both mass and energy with
its surroundings
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19. Can a system be in steady state yet have the fluid passing through it undergoing
a phase change? Reconcile your answer with the definition of steady state.
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Yes. Steady state occurs in a system when the fluid properties at a given point
remain constant with respect to time. A fluid undergoing a phase change will
have properties that change from point to point. However, to determine if the
system is in steady state, we must concentrate on a single point over time.
Change of Phase
20. Describe the difference between an intensive and an extensive property. Give 2
examples of each type of property.
Intensive properties are independent of the amount of mass present. Extensive
properties are a function of the amount of mass present. Examples of intensive
properties are pressure, temperature, and density. Examples of extensive
properties are volume, weight, and energy.
21. A system contains 250 lbm of saturated liquid and 10 lbm of saturated
vapor. What is the quality of the system?
mvapor
X 10lbm 0.038 or 3.8%
mliquid + mvapor 250lbm + 10lbm
Property Diagrams and Steam Tables
22. Steam enters a turboexpander as a saturated vapor at 500 psia and is expanded
at constant entropy to 5 psia. Using the Mollier diagram in Appendix A (Figure A-
1), find the h for this process.
From the Mollier diagram: Btu
1205 895 310 lbm
23. Use the excerpt from the steam tables in Appendix A (Figure A-2) to find h, ν
, and s for water:
Saturated liquid, P = 350 psia
Btu ft 3 Btu
h 409.8 0.01912 s 0.6059
lbm lbm lbm R
Saturated vapor, P = 400 psia
h Btu ft
1204.6 3 s 1.4847 Btu
1.16095
lbm lbm lbm R
Saturated liquid, T = 468 F
h 450.7 Btu ft
3 s 0.6502 Btu
0.01976
lbm lbm lbm R
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Superheated steam, P = 400 psia and T=700 F
h Btu ft 3
1363.4 1.6499 s Btu
1.6406
lbm lbm lbm R
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24. Use the steam tables and the concept of quality to find h and for water at a
pressure of 260 psia if entropy is known to be 0.725 Btu
lbm R
.
s s Xs sWV 0.725 0.5722
sf X 16%
WV f fg
sfg 0.9508
h h Xh 379.9 0.16 821.6 Btu
511.4
WV f fg
lbm
ft 3
WV Xfg 0.01870 0.16 1.75548
0.29958
lbm
f
25. Calculate specific internal energy for a 200 psia system of saturated liquid.
Hint: Review the definition of enthalpy.
h u P u h P
Btu lbf ft 3 144in Btu Btu
u 355.5 (200 2 )(0.01839 )( 2 )( ) 354.82
lbm in lbm 778ft lbf lbm
ft 2
First Law of Thermodynamics
26. State the First Law of Thermodynamics.
Energy can neither be created nor destroyed, only altered in form.
27. The following schematic of a simple Rankine cycle consists of steam leaving a
boiler at T=550 F and P=400 psia and passes through a turboexpander where
it does work and exhausts with an enthalpy of 932 Btu/lbm. The exhaust is then
condensed to an enthalpy of 85 Btu/lbm before being pumped back into the
boiler.
T=550 F
P=400 psia
h=?? Btu/lbm
h=932 Btu/lbm
h=85 Btu/lbm
Given Btu lbm ˙
= 4.15×106 an d Q
W˙ turb
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boil
Btu t e mass flow rate of the lbm
er7
,find h
system (m˙ system ), the total heat transfer out at the condenser(Q˙ Cond ),and the enthalpy
of the fluid after leaving the pump and before entering the boiler.
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W˙ m˙ (h)
m˙ W˙ turb
turb system turb system
(h)turb
Btu
4.15 106
lbm
hr 1.2 104
system hr
m˙ (1277.5 932) Btu
lbm
Q˙ m˙ (h) lbm Btu
1.2 104 (932 85) Btu
1.02 107
condenser system condenser
hr lbm hr
Btu
˙ 1.43 107
Btu
Q˙ Q hr
m˙
(h) h boiler 1191.67
boiler system boiler boiler
m˙ 4 lbm lbm
1.2
system 10 hr
h h h h 1277.5 1191.67 Btu
boiler steam water entering boiler water entering boiler
85.8
lbm
Second Law of Thermodynamics
28. What is the maximum possible cycle efficiency of a heat engine operating
between a heat source at 400 F and a heat sink at 32 F?
(32 460)
max 1 1 1.572 42.8%
TC (400 460)
TH
29. An inventor claims to have invented a device which absorbs 2500 Btu of heat
and produces 2000 Btu of work. If the heat sink for the device is ice water (32 F),
what would be the minimum source temperature?
actual Wnet 2000Btu TC (given)
Q 2500Btu 80% max 1 T
in H (need to solve)
Setting max equal to actual gives T
H (minimum)
(32
460)R 1
0.80 TH (minimum) (32 460)R 2460 R 2000 F
TH (minimum) 1 0.80
30. What is the efficiency of a turbine which receives dry, saturated steam at 100
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psia and exhausts a wet vapor at 1 psia, while producing 230 Btu/lbm of real
work?
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wreal Btu
h
230 lbm
turbine w h
ideal stm exhideal
hsat.stm@100 psia 1188 from Mollier diagram or steam table
lbm
Btu
h 895
Btuexh @1 psia
from intersection of constant entropy
ideal lbm
process line with 1 psia line on Mollier diagram.
230 Btu
turbine lbm
.785 78.5%
(1188 895) lbm
Btu
Compression Processes
31. State the ideal gas law. Explain the meaning of each symbol.
P RT where P is the gas pressure in absolute units, is the specific
volume of the gas, R is a constant for a given gas, and T is the absolute
temperature of the gas.
32. When can a fluid be considered incompressible? Give an everyday example
of such a fluid.
A fluid is considered incompressible when it is in the liquid state, or when it is a
gas at high speed. (Speed greater than 1/3 the speed of sound in the gas.)
Liquid water is an everyday fluid which is considered to be nearly
incompressible.
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