Physics 7: Fluids
Practice Problems
1.
2.
3.
4.
5.
A. Static Fluid
If one material has a higher density than another, does this
mean that the molecules of the first material must be more
massive than those of the second?
(A) yes
(B) no
Consider what happens when you push both a pin and a
blunt end of a pen against your skin with the same force.
What will determine whether your skin will be punctured?
(A) the pressure on your skin
(B) the net applied force on your skin
You are walking out on a frozen lake and you begin to hear
the ice cracking beneath you. What is your best strategy
for getting off the ice safely?
(A) stand absolutely still and don't move a muscle
(B) slide your feet (with lifting them) to move towards shore
(C) lie down flat on the ice and crawl toward shore
While swimming near the bottom of a swimming pool, you
let out a small bubble of air. As the bubble rises toward the
surface, what happens to its diameter?
(A) decreases (B) same
(C) increases
Three containers are filled with water to the same height
and have the same surface area at the base, but the total
weight of water is different for each. Which container has
the greatest total force acting on the base?
(A)
(B)
(C)
(D) tie
When a hole is made in the side of a water bottle, water
flows out and follows a parabolic trajectory. If the container
is dropped in free fall, the water flow will
(A) diminish
(B) stop
(C) go in a straight line
(D) curve upward
7. When you drink liquid through a straw, which below is
primarily responsible for this to work?
(A) water pressure
(B) gravity
(C) inertia
(D) atmospheric pressure
8. You put a straw into a glass of water, place your finger
over the top so no air can get in or out, and then lift the
straw from the liquid. You find that the straw retains some
liquid. How does the air pressure P inside the straw
compare to atmospheric pressure PA?
(A) P > PA
(B) P = PA
(C) P < PA
9. In a mercury barometer at room pressure, the height of the
mercury column in a glass tube is 760 mm. If another
mercury barometer is used that has a larger diameter tube,
how high will the column of mercury be in this case?
(A) greater
(B) same
(C) less
10. Thermometers often use mercury or alcohol in a thin glass
tube, but barometers never use alcohol. Why?
(A) mercury is less flammable
(B) mercury's color is easier to see
(C) mercury is less toxic than alcohol
(D) mercury is more dense than alcohol
11. Imagine holding two identical bricks in place under water.
Brick A is just beneath the surface of the water, while brick
B is held about two feet down. The force needed to hold
brick B in place is
(A) greater
(B) same
(C) less
Questions 12-13 A beaker filled completely with water is placed
on a scale and weighs 29 N. A block is carefully placed in
the beaker at the same time water overflows out of the
beaker.
12. The block is made of wood and floats in the water. When
placed on the scale the beaker and floating block will weigh
(A) < 29 N
(B) = 29 N
(C) > 29 N
6.
Name __________________________
13. The block is made of aluminum and sinks. When placed on
the scale the beaker and sunk block will weigh
(A) < 29 N
(B) = 29 N
(C) > 29 N
14. A raft carrying a large tank is floating in a pool. The tank is
then thrown overboard and sinks. What happens to the
water level in the pool with respect to the pool side?
(A) rise
(B) same
(C) drop
Questions 15-19 Object A floats in pail of water with ¾ of its
volume submerged.
15. What is the ratio of the density of object A to that of water?
(A) ¼
(B) ¾
(C) 4/3
(D) 4
16. Object A is now placed in oil with a density half that of
water. What fraction of object A is above the fluid line?
(A) 0
(B) ¼
(C) ½
(D) ¾
17. Water is added to the empty pail to a level above the top of
object A, the object will
(A) move up slightly
(B) stay at the same place
(C) move down slightly
(D) float to the top
18. Oil is added to the pail with water from question 17 to a
level above the top of object A, the object will
(A) move up slightly
(B) stay at the same place
(C) move down slightly
(D) float to the top
19. Object A, in a pail of water, is observed on the moon. What
fraction of its volume is submerged?
(A) < ¾
(B) = ¾
(C) > ¾
Questions 20-21 A helium balloon is placed in an inverted airfilled jar, which rests on a table. The balloon floats to the
top of the jar.
20. If the air is replaced with helium, where will the balloon be?
(A) at the top
(B) in the middle (C) at the bottom
21. If the jar if lifted off the table, but the helium remains in the
jar, where will the balloon end up?
(A) top
(B) middle (C) bottom (D) ground
22. A rubber balloon is filled with water and just enough
trapped air so that it floats. The balloon is placed in a glass
cylinder also filled with water and is sealed with a flexible
cap. When you push down on the flexible cap, the balloon
(A) sinks down (B) stays put
(C) rises up
23. How does a liquid differ from a solid or gas?
24. What is the mass of a piece of gold ( = 1.93 x 104 kg/m3)
that has a volume of 22 cm3?
25. Why is the formula P = gh useful for liquids but not gases?
26. At what depth in water is the added pressure equal to 1
atm (1.0 x 105 Pa)?
27. What is the absolute air pressure, in Pa, in a tire that has a
gauge pressure reading of 30 lbs/in2? (1 atm = 14.7 lbs/in2)
28. a.
1,000 N of force is used to raise a 10,000 N car. What
is the ratio of the cross-sectional area of the lift piston
to the force piston (A2/A1)?
b.
How far does the force piston move to lift the car 2 m?
29. How much mass (M) must be added to a diver (85-kg,
0.090-m3) to allow him to float under water?
30. What percentage of the volume of a floating iceberg is
above sea water? (ice = 920 kg/m3, sea water = 1030 kg/m3)
31. What volume of helium is needed to lift a load of 800 kg?
(air = 1.29 kg/m3, He = 0.18 kg/m3)
32. What is the specific gravity of a piece of metal that has a
mass of 125 g in air and 78.7 g in water?
33. A crown's "weight" in air is 14.7 kg. What is its "weight"
under water if it is made of
40. Water flows through a 1-cm diameter pipe connected to a
½-cm diameter pipe. Compared to the speed of the water
in the 1-cm pipe, the speed in the ½-cm pipe is
(A) ¼
(B) ½
(C) 2
(D) 4
41. A blood platelet drifts along with the flow of blood through an
artery that is partially blocked. As the platelet moves from the
wide region into the narrow region, the blood pressure
(A) increases
(B) same
(C) decreases
42. A person's blood pressure is generally measured on the
arm, at approximately the same level as the heart. How
would the results differ if the measurement were made on
the person's leg instead?
(A) higher
(B) same
(C) lower
43. Smoke is drawn up a chimney on a windy day. The draw
on a windy day compared to a calm day is
(A) faster
(B) same
(C) slower
44. Consider the diagram in your notes (B3).
a. How many times bigger is A1 compared to A2 if the
diameter, d1, is two times the diameter, d2?
gold (s.g. = 19.3)
lead (s.g. = 11.3)
b.

34. The weight of a 300 N piston compresses gas in a tank.
a. What is the pressure on the gas generated by the
piston, which has a radius of 0.050 m?
b.
What is the total pressure in the tank if the
atmospheric pressure is 1 x 105 Pa?
35. What is the water pressure in a pipe that is 45 m below the
water level in the city's water storage tank?
36. In a hydraulic system, cylinder A with a 100 cm2 cross
section is connected by fluid to cylinder B with a 10 cm2
cross section. 2000 N of force push on the cylinder A's
piston. Determine
a. the force generated on cylinder B's piston?
b.
the distance piston B moves if piston A moves 5 cm.
37. What is the density of a log when 65% of the volume is
submerged in water ( = 1000 kg/m3)?
How many times faster is v2 compared to v1?
45. Consider the water pipe in your notes (B4). What is P2 when
P1 = 3 x 105 Pa, v1 = 2 m/s, v2 = 5 m/s, y1 = 0 m, y2 = 4 m?
46. A water leaks out of a hole 5 m below the surface in a tank.
a. What is the velocity of water that leaks out of the tank?
b.
What is the radius of the hole in the water tank if the
volume rate flow out of the leak is 3 x 10-3 m3/s?
47. a.
Air flows past the upper surface of an airplane wing at
250 m/s and past the lower surface of the wing at 200
m/s. The density of air is 1.0 kg/m3 and the area of
the wing is 20 m2. What is the net lift on the wing?
b.
Racing cars have a rear spoiler, which is able to keep
the car from lifting up at high speeds. Describe the
design of the spoiler.

48. When a truck passes you on the left, your car initially is
pushed right then pulled left. Why?
38. An aluminum ( = 2700 kg/m3) object has a mass of 27 kg.
The object is attached to a string and immersed in a tank
of water. Determine
a. the volume of the object.

b.
the tension in the string.
39. What volume of helium will support a load of 1000 kg?
(air = 1.29 kg/m3, He = 0.18 kg/m3)
B.
Fluid Flow
49. Water flows at a rate of 0.5 m/s through a 4-cm diameter
pipe on the first floor of a house.
a. What is the cross-sectional area of the pipe?
b.
What is the volume flow rate in the 4-cm pipe?
c.
What is the mass of one molecule in kg?
c.
What is the velocity of the water in a 2.6-cm diameter
pipe on the second floor of the house.
d.
What is the average kinetic energy of a molecule?
e.
What is the kinetic energy of a mole?
d,
The pressure in the 4-cm pipe is 3 atm. What is the
pressure in the 2.6 cm section that is elevated 3 m?
f.
What is the average speed?
50. Air ( = 1 kg/m3) passes over a roof at 60 m/s. Determine
a. the pressure difference between the attic air and the
air passing over the roof.
b.
the upward force exerted on the roof (area = 300 m2).
62. Consider one mole of helium gas at room temperature
(22oC) and pressure (1.0 x 105 Pa).
a. What is the volume (in m3)?
b.
What is the volume (in m3) of one helium atom with an
atomic radius is 5 x 10-11 m?
C. Kinetic Theory—Gases
51. Which is the largest unit, 1o C, 1 K or 1o F?
c. What is the volume (in m3) of one mole of helium
(A) 1oC
(B) 1 K
(C) 1oF
(D) 1oC and 1 K
atoms?
52. It turns out -40o C is the same temperature as -40o F. Is
there a temperature where the Kelvin and Celsius scales
agree?
d. What percentage of the total volume (part a) is taken
(A) yes 0oC
(B) yes, -273oC
up by the helium atoms (part c)?
(C) yes, 0 K
(D) no
53. Which has more molecules, one mole of N2 or one mole of
O2?
e. What is the volume when the pressure is increased to
(A) N2
(B) O2
(C) tie
2.0 x 105 Pa and the temperature is raised to 44oC?
54. Which weighs more, one mole of N2 or one mole of O2?
(A) N2
(B) O2
(C) tie
55. Two identical cylinders at the same temperature contain
the same gas. If A contains three times as much gas as B,
63. A 0.01 m3 vessel contains 0.02 kg of an ideal gas at 50oC
which cylinder has the higher pressure?
and a pressure of 3 x 105 Pa. Determine the
(A) A
(B) B
(C) tie
a. kinetic energy per molecule
56. Two identical cylinders at the same pressure contain the
same gas. If A contains three times as much gas as B,
which cylinder has the higher temperature?
b. moles of gas are in the vessel (R = 8.31).
(A) A
(B) B
(C) tie
57. Two cylinders at the same temperature contain the same
gas. If A has twice the volume and half the number of
moles as B, how does the pressure of A compare with the
c. molar mass of the gas.
pressure of B?
(A) PA = ¼PB
(B) PA = ½PB
(C) PA = 2PB
58. A partially filled, sealed plastic water bottle sits out in the sun,
D. Heat
heating the air inside. What happens to the bottle?
64. Two objects are made of the same material, but have
(A) it expands (B) nothing
(C) it shrinks
different masses and temperatures. If the objects are
59. What happens to the volume of a balloon if you put it in the
brought into thermal contact, which one will have the
refrigerator?
greatest change in temperature?
(A) it expands (B) nothing
(C) it shrinks
(A) the one with the higher initial temperature
60. In the formulas K = 3/2RT and PV = nRT
(B) the one with the lower initial temperature
a. The value of R is (_________).
(C) the one with the greater mass
b. Why must you use the Kelvin temperature scale for
(D) the one with smaller mass
these calculations?
65. Two different objects receive the same amount of heat.
Which of the following choices is NOT a reason why the
objects may have different changes in temperature?
c. What is the Kelvin temperature for 25oC?
(A) they have different initial temperature
(B) they have different mass
(C) they have different specific heat
66. Two equal-mass liquids, initially at the same temperature,
61. Consider oxygen gas (O2) at 22oC.
are heated for the same time over the same stove. You
a. What is the temperature in Kelvin?
measure the temperatures and find that one liquid has a
higher temperature than the other. Which liquid has a
higher specific heat?
b. What is the mass of one mole in kg?
(A) cooler one (B) hotter one (C) tie
67. The specific heat of concrete is greater than that of soil. A
baseball field and the surrounding parking lot are warmed
up during a sunny day. Which would you expect to cool off
faster in the evening when the sun goes down?
(A) field
(B) lot
(C) tie
68. Water has a higher specific heat than sand. Therefore, on
the beach at night, breezes would blow
(A) from ocean to beach (B) from beach to ocean
69. 1 kg of water at 100oC is poured into a bucket that contains
4 kg of water at 0oC. Find the equilibrium temperature.
(A) 10oC
(B) 20oC
(C) 50oC
(D) 80oC
70. A 1-kg block of silver (c = 234 J/kg•K) is heated to 100oC,
then dunked in a tub of 1 kg of water (c = 4186 J/kg•K) at
0oC. What is the final equilibrium temperature?
(A) < 50oC
(B) 50oC
(C) > 50oC
71. Given your experience of what feels cooler when you walk
on it, which surface has the higher thermal conductivity?
(A) rug
(B) tile
72. Two drinking glasses are stuck, one inside the other. How
would you get them unstuck?
(A) run hot water over them both
(B) run hot water over the inner glass
(C) run hot water over the outer glass
73. What happens to a hole in a sheet of metal that is heated?
(A) expand
(B) contract
74. Write the words that are defined below.
is the total energy of a body
measures the "warmth" of an object
is transferred between two bodies at
different temperatures
75. Fill in the missing word about heat transfer.
When two objects are the same
temperature __ heat is transferred
When heat is transferred to a system, it
either increases the systems __ or the
system performs __
When two objects are at different
temperatures, heat naturally flows from
the __object to the __ object.
76. Write the form of heat flow described below.
Energy transfer through collisions
81. How much heat is needed to raise the temperature of 100 g
of lead (c = 130 J/kg•K) from 20oC to 25oC?
82. 120 g of an alloy is heated to 200oC then placed in 500 g
of 25oC water (c = 4200 J/kg•K) contained in a 200 g
aluminum cup (c = 900 J/Kg•K). The final temperature is
31.5oC. What is the specific heat of the alloy?
83. How much time will it take to raise the temperature of 500
mL of water from 22oC to 100oC using a 750 W heater?
84. What is the diameter of a hole cut in steel ( = 12 x 10-6 oC-1)
when it is heated to 600oC if it is 0.1000 m at 20oC?
85. How much heat is needed to raise the temperature of a 2kg aluminum (c = 900 J/kg•K) vat filled with 20 kg of
alcohol (c = 2400 J/kg•K) from 10oC to 75oC?

86. What is the final temperature when 150 cm3 of 75oC water
(c = 4200 J/kg•K) is added to a 50-g Al (c = 900 J/kg•K)
cup at 25oC?
E. Heat Engines
87. What is the change in internal energy of a system if 2000 J
of heat is added to the system and the system does 1000 J
of work to the surroundings?
88. How much heat is added to one mole of helium for each of
the following?
a. Isometric change from 200 K to 400 K.

b.
Isobaric change from 200 K to 400 K.
c.
Isothermic change that does 1000 J of work to the gas.
d.
Adiabatic change that does 1000 J of work to the gas.
Photons are emitted from hot objects
Hot fluid moves to cooler location
77. What factors affect the rate that heat is conducted through
a piece of glass?
78. Write the form of heat transfer that is reduced by the
following home construction elements.
Double-paned windows
Overhangs along the south side
89. The temperature of 0.0010 m3 of He ( = 0.179 kg/m3) is
increased from 250 K to 750 K at constant volume.
a. How many moles of helium are heated?
Weather striping around windows and doors
79. A 20-cm long bimetal strip of brass ( = 19 x 10-6 oC-1) and
aluminum ( = 26 x 10-6 oC-1) is heated from 22oC to
150oC. How much longer is the aluminum side?
80. Why is the formula, Q = mcT, used for solids and liquids,
but not gases?

b.
How much heat is required?
c.
How much power is needed to heat the helium in 1 s?
90. Which process (isobaric, isothermic, or adiabatic) would
use the least amount of work to compress a gas? Explain.
91. The initial conditions for 1 mole of monatomic gas are
0.10 m3 and 1.0 x 105 Pa.
a. What is the temperature of the gas?
b.
The gas pressure is doubled isometrically.
(1) What is the new temperature?
(2) How much work is done to the gas, Win?
(3) How much heat did the gas absorb?
(4) What is the change in internal energy, U?
c.
The gas is returned to its initial condition and then its
volume is doubled isobarically.
(1) What is the new temperature?

(2) How much work is done to the gas, Win?
92. Answer the questions for the Isothermal-adiabatic cycle in
your notes (2a).
a. Starting from point a, indicate in the diagram whether
the change +, –, or 0 (unchanged).
Process
T
U = Qin + W in
1.
Isothermal expansion
2.
Adiabatic expansion
3.
Isothermal compression
4.
Adiabatic compression
b.
Change
Check the appropriate step.
1
2
3
4
generate power for the heat engine
heat gained to the system
heat lost by the system
c. What does the region enclosed by the cycle represent?

93. One mole of gas is initially at point A (100 kPa, 0.01 m3).
The gas is heated at constant volume until it reaches point B
(200 kPa), and then expands at constant pressure to point C
(0.02 m3). Heat is removed at constant volume to point D
(100 kPa), then contracts at constant pressure to point A.
a. label points A, B, C and D.
P (kPa)
(3) How much heat did the gas absorb?
200
(4) What is the change in internal energy, U?
100
b.
d.
The gas is returned to its initial condition and then
1.0 x 104 J of heat is added to the gas isothermically.
(1) What is the new temperature?
(2) How much work is done to the gas, Win?

(3) What is the change in internal energy, U?
A
C
D
c. Complete the chart by calculating each value.
Step
U
=
Qin
+
Win
AB
The gas is returned to its initial condition and then the
1.0 x 104 J of work is done to the gas adiabatically.
(1) How much heat did the gas release?
BC
(2) What is the change in internal energy, U?
CD

DA
f.
V (m3)
B

e.
0.01
0.02
What are the temperatures at each point?
Graph each change described in parts b-e below.
2 Po
Change
d. Why must the change in Qin + Win = 0?
Po
Vo
2 Vo
Complete the chart for the processes b-e by indicating
whether the value is +, – or 0 (unchanged)
Qin
Win
Process
U
isometric (b)
g.
isobaric (c)
isothermic (d)
adiabatic (e)
e.
Calculate the area inside the box diagram?
f.
Determine the first law efficiency?
g.
Determine the Carnot efficiency?
94. An ideal gas undergoes a cyclic process as shown on the
graph of pressure P versus volume V.
101. One mole of gas initially at point A (50 kPa, 0.01 m3),
increases pressure isometrically to point B (100 kPa), then
expands isothermically to point C (0.02 m3), and finally is
compressed isobarically to point A. The work done by the
gas during one cycle is 200 J.
a. Sketch the heat cycle.
P (kPa)
100
50
Indicate in the chart whether the change is positive (+),
negative (–), unchanged (0), or can't tell (?).
Process
T
U
=
Qin
+
Win
AB
b.
BC
A
V (m3)
0.01
0.02
What are the temperatures at each point?
CD
DE
B
EA
C
Change
95. A power plant generates 120 MW (1.2 x 108 J/s) of
electricity at 40% efficiency. Determine
a. The electric energy generated in 1 hour.
c. Complete the chart.
Step
U
=
Qin
+
Win
AB
BC
b.
The energy supplied to the power plant in 1 hour.
(Hint: electric output = work)
CA
c.
Heat discarded by the power plant.
Change
d. In which step is work done to the gas?
d.
The change in temperature of 1 x 108 kg of water (c =
4200 J/kg•K) that absorb all the discarded heat in 1 hr.
e.
What is the total heat added to the gas?
f.
How much heat is exhausted during one cycle?
g.
Determine the first law efficiency?
h.
Determine the Carnot efficiency?
96. What is U for an isothermic process?
97. How is work represented on a PV diagram?

98. Which process would require the most work to double the
volume of a gas, isothermic, adiabatic or isobaric?
99. How much work is done on 0.30 moles of gas during an
adiabatic expansion that drops the temperature from 1150
K to 400 K?
102. An ideal gas undergoes a cyclic process as shown on the
graph of pressure P versus volume V.
100. One mole of an ideal gas, initially at 273 K, is heated at a
constant pressure of 2 x 105 Pa until the volume doubles.
Determine the
a. initial volume of the gas (R = 8.31 J/mol•K).
b.
work done to the gas during the expansion.
c.
change in internal energy of the gas.
d.
Heat added to the gas.
Indicate in the chart whether the change is positive (+),
negative (–), unchanged (0), or can't tell (?).
Process
T
U
=
Qin
+
Win
XY
YZ

ZX
Change
103. A engine operates at an input temperature of 1000 K while
producing 1000 J of useful work per hour. The engine has a
Carnot efficiency of 30 % and a first law efficiency of 20 %.
Determine the
a. input heat used each hour.
b.
exhaust heat produced each hour.
c.
exhaust temperature.
Practice Multiple Choice
Briefly explain why the answer is correct in the space provided.
Questions 1-2 The spring scale reads 0.45 kg when
the rock is suspended in air and 0.36 kg when
the rock is fully submerged in water.
1. The buoyant force that the fluid exerts on the
object is
(A) 1.3 N
(B) 0.9 N
(C) 0.75 N
(D) 0.33 N
2.
3.
4.
5.
8.
A rock is thrown into a swimming pool that is at a uniform
temperature. While the rock sinks, the buoyant force
(A) is zero
(B) increases
(C) decreases
(D) is constant
Questions 9-11 Two pistons are connected in a hydraulic lift. The
diameter of the large piston is ten times that of the small.
9. How many times larger is the cross-sectional area of the
larger piston compared to the smaller?
(A) 10
(B) 20
(C) 50
(D) 100
10. A 500-N force is applied to the smaller piston. What load
can be lifted by the larger piston?
(A) 5,000 N
(B) 50,000 N
(C) 500,000 N
(D) 5,000,000 N
(D) 5,000
An object weighs 15,000 N. When it is submerged in a
liquid that has a density of 1500 kg/m3, its apparent weight
is 7500 N. What is the density (in kg/m3) of the object?
(A) 1,500 (B) 2,000 (C) 3,000 (D) 6,000
Two dams are alike in every respect (i.e. height, width and
thickness of dam) except the length of the lake behind the
dam. The first lake extends 1 km away from its dam; the
second 5 km. The force exerted on the first dam is:
(A) equal to the force on the second dam
(B) greater than the force on the second dam
(C) less than the force on the second dam
Each beaker is filled to the same depth with the same
liquid and the area of the flat bottom is the same for each.
Which ranks the beakers from greatest to least force
exerted by the liquid on the flat bottom?
(A) I > III > II > IV
(B) I > IV > III > II
(C) II > III > IV > I
(D) force on each is the same
6.
What is the absolute pressure (in Pa) 3 m down in a
swimming pool, when atmospheric pressure is 1 x 105 Pa?
(A) 3 x 104 (B) 7 x 104 (C) 1.1 x 105 (D) 1.3 x 105
11. If the load is lifted 2 m, how far is the smaller piston moved?
(A) 0.2 m (B) 2 m
(C) 20 m
(D) 200 m
kg/m3)
The density (in
of the rock is
(A) 200
(B) 800
(C) 1,250
7.
What is the force exerted by a wind, which generates a
pressure difference of 3 x 104 Pa, on the 3 m by 20 m side
of a house trailer?
(A) 0.5 N
(B) 500 N (C) 1800 N (D) 1.8 x 106 N
Questions 12-13 A 1500-kg stone of volume 0.5 m3 is lowered to
the bottom of a lake on the end of a rope.
12. What buoyant force acts on the stone?
(A) 5 N
(B) 50 N
(C) 500 N (D) 5,000 N
13. What is the tension when the stone is submerged?
(A) 3,500 N
(B) 5,000 N
(C) 10,000 N
(D) 15,000 N
14. Water is flowing through a pipe with a cross-sectional area
of 30 cm2 at a velocity of 4 m/s. What is the velocity of the
water in a section of the pipe where the cross-sectional
area is 50 cm2?
(A) 1.2 m/s (B) 3.6 m/s (C) 2.4 m/s (D) 4.8 m/s
15. Water is pumped into one end of a long pipe at a rate of 50
liters per minute. The water is emerges from the other end
of the pipe at a rate of 20 liters per minute. The reason for
this decrease in volume flow rate is
(A) the water is being pumped uphill
(B) the pipe diameter is not the same at the two ends
(C) there is friction in the pipe
(D) there is a leak in the pipe
16. An ideal gas confined in a box initially has pressure P. If
the absolute temperature of the gas is doubled and the
volume of the box is quadrupled, the pressure is
(A) ⅛ P
(B) ¼ P
(C) ½ P
(D) P
17. A pitched baseball, which rotates counterclockwise about a
vertical axis as seen from above, will curve:
(A) to the pitcher's right (B) to the pitcher's left
(C) upward
(D) downward
18. The absolute temperature of a sample of monatomic ideal
gas is doubled at constant volume. What effect, if any, does
this have on the pressure and density of the sample of gas?
Pressure
Density
(A) Remains the same
Remains the same
(B) Remains the same
Doubles
(C) Doubles
Remains the same
(D) Doubles
Is 4 times greater
Questions 19-20 An ideal gas molecule at absolute temperature,
T, has kinetic energy, K, and velocity, v.
19. What is the kinetic energy at 4T?
(A) ¼K
(B) ½K
(C) 2K
(D) 4K
20. What is the velocity at 4T?
(A) ¼v
(B) ½v
(C) 2v
(D) 4v
21. If wind blows at 30 m/s over your house, the net force on
the roof (area = 400 m2) is
(A) 100,000 N
(B) 150,000 N
(C) 180,000 N
(D) 200,000 N
22. Water flows out of a hole at 4 m/s. What is the height of
the water above the hole inside the bucket?
(A) 0.8 m (B) 1.25 m (C) 2.5 m (D) 1.5 m
23. The area of an airplane wing is 100 m2. What is the lift
force on the wing when the speed of air below and above
the wing 200 m/s and 250 m/s respectively?
(A) 2,500 N
(B) 11,250 N
(C) 4.2 x l05 N
(D) 1.125 x l06 N
29. A T-shaped tube with a constriction is inserted in a vessel
containing a liquid.
What happens if air is blown through the tube from the left?
(A) The liquid level in the tube rises up into the tube.
(B) The liquid level in the tube falls below the level of the
surrounding liquid.
(C) The liquid level in the tube remains where it is.
(D) The air bubbles out at the bottom of the tube.
30. A sample of an ideal gas is in a tank of constant volume.
The sample absorbs heat energy so that its temperature
changes from 300 K to 600 K. If v1 is the average speed of
the gas molecules before the absorption of heat and v2 is
their average speed after the absorption of heat, what is
the ratio v2/v1?
(A) ½
(B) 1
(C) √2
(D) 2
31. A square steel plate with 1.00 m long sides has a hole in
its center 0.100 m in diameter. If the plate is heated until its
sides become 1.01 m long, the diameter of the hole will be
(A) 0.090 m (B) 0.099 m (C) 0.100 m (D) 0.101 m
32. Which of the following statements is NOT a correct
assumption of the classical model of an ideal gas?
(A) The molecules are in random motion.
(B) The volume of the molecules is negligible compared
with the volume occupied by the gas.
(C) The molecules obey Newton's laws of motion.
(D) The collisions between molecules are inelastic.

24. At best, a person can reduce the pressure in the lungs
about 1 x 104 Pa below atmospheric pressure. How high
can a person suck water up a straw?
(A) 0.1 m (B) 0.3 m (C) 1.0 m (D) 3.0 m
33. If the gas in a container absorbs 275 J of heat, has 125 J of
work done on it, and then does 50 J of work, what is the
increase in the internal energy of the gas?
(A) 100 J
(B) 200 J
(C) 350 J
(D) 400 J
25. If a crown of density 14,000 kg/m3 weights 140 N in air, the
force needed to support it when submerged in water is:
(A) 100 N (B) 130 N (C) 140 N (D) 150 N
34. The temperatures on each side of a window
with area A and thickness d are T2 and T1,
respectively. Increasing which of the
following would decrease the rate that
heat is conducted through the glass?
(A) T2 – T1 only
(B) d only
(C) A only
(D) A and T2 – T1
26. A rowboat has a volume of 1.5 m3 and a mass of 40 kg.
How many 70-kg people can the boat support?
(A) 15
(B) 19
(C) 20
(D) 21
cm3
27. An object floats in water and displaces 150
of water.
The same object floats in oil, displacing 375 cm3 of that oil.
The density (in kg/m3) of the oil is:
(A) 1,500 (B) 1,100 (C) 600
(D) 400
Questions 35-36 A 1.5-kg piece of metal (c = 200 J/kg•K) and
initial temperature of 100oC is dropped into an insulated jar
that contains 3.0-kg of liquid (c = 1,000 J/kg•K) and initial
temperature of 0oC. The piece of metal is removed after 5
s, at which time its temperature is 20oC.
35. The temperature of the liquid after the metal is removed is
(A) 0oC
(B) 4oC
(C) 8oC
(D) 10oC
28. Water is flowing through a horizontal pipe with a constriction.
At one end of the pipe we have A1 = 10 cm2, v1 = 4 m/s, and
36. The average rate at which heat is transferred while the
P1 = 500 kPa. In the constriction of the pipe we have
piece of metal is in the liquid is
A2 = 2 cm2. The pressure (in kPa) in the constriction is:
(A) 4,000 J/s
(B) 4,800 J/s
(A) 120
(B) 308
(C) 480
(D) 690
(C) 6,000 J/s
(D) 9,600 J/s
Questions 37-38 An ideal gas initially at temperature To,
pressure Po, and volume Vo is compressed to one-half its
initial volume. The process may be adiabatic (process 1),
isothermal (process 2), or isobaric (process 3).
37. Which process does the most mechanical work on the gas?
(A) 1
(B) 2
(C) 3
(D) all the same
Questions 44-45 A thermodynamic system is taken from an initial
state X along the path XYZX.
44. Which is negative for the process XY?
(A) Qin
(B) Win
(C) U
(D) Qin and U
45. For which is U negative?
(A) XY
(B) YZ
(C) ZX
(D) XYZX
Questions 46-47 An ideal gas undergoes the process below.
38. Which process results in the highest temperature?
(A) 1
(B) 2
(C) 3
(D) all the same
39. Which is always a characteristic of an adiabatic process?
(A) The temperature does not change (T = 0).
(B) The pressure does not change (P = 0).
(C) The internal energy does not change (U = 0).
(D) No heat flows into or out of the system (Q = 0).
46. During which process is no work done on or by the gas?
(A) AB
(B) BC
(C) CD
(D) DE

40. An engine absorbs 100 J of heat and exhausts 60 J. What
is the efficiency of the engine?
(A) 40 %
(B) 60 %
(C) 67 %
(D) 150 %
41. The maximum efficiency of a heat engine that operates
between temperatures of 1500 K in the firing chamber and
600 K in the exhaust chamber is most nearly
(A) 33 %
(B) 40 %
(C) 60 %
(D) 67 %
42. Three identical samples of an ideal gas are taken from initial
state I to final state F along the paths IAF, IF, and IBF.
47. At which point is the gas at its highest temperature?
(A) A
(B) B
(C) C
(D) D
Questions 48-50 A cylinder with a movable piston contains 0.1
mole of a monatomic ideal gas. The gas, initially at state a,
can be taken through either of two cycles, abca or abcda.
The following information is known about this system.
(1) For path c  a: Qin = 685 J
(2) For path c  a: Win = -120 J
(3) For path a  b: U = -450 J
(4) For path b  c: Win = 75 J
Use the following options.
(A) 565 J
(B) 805 J
(C) 450 J
48. What is U for the path c  a?
Which must be true?
(A) The work done by the gas is the same for all paths.
(B) The heat absorbed by the gas is the same for all paths.
(C) The change in internal energy is the same for all paths.
(D) The expansion along path IF is isothermic.
(D) 150 J
49. How much heat is removed for the path a  b?

50. How much work is done in the process c  d  a?

43. A block (c = 100 J/kg•K) falls 100 m. If half of the potential
energy lost by the fallen block is converted to internal
energy, the temperature change of the block is most nearly
(A) 1 K
(B) 5 K
(C) 10 K
(D) 25 K
Practice Free Response
1.
A 0.6-kg object at 100oC is dropped into a 0.1-kg container
(c = 840 J/kg•K) that holds 0.2 kg of water (c = 4190 J/kg•K)
at 20oC. The system reaches an equilibrium temperature of
50oC. Determine
a. the heat gained by the water.
b.
the heat gained by the glass container.
d
the heat added to the gas.

c.
the heat lost by the metallic object.
d.
the specific heat of the metallic object.
e.
5.
2.
A large rectangular raft ( = 650 kg/m3) is floating on a
lake. The surface area of the top of the raft is 8.2 m2 and
its volume is 1.80 m3. The density of water is 1000 kg/m3.
A = 8.2 m2
h
the final temperature of the gas.
The large container is filled with water ( = 1000 kg/m3). A
small hole of area 2.5 x 10-6 m2 is opened in the side of the
container a distance h below the water surface, which
allows a stream of water to flow through the hole and into a
beaker. At the same time, water is also added to the
container so that h remains constant. The amount of water
collected in the beaker in 2.0 minutes is 7.2 x 10 -4 m3.
water line
3.
a.
Calculate the height h of the portion of the raft that is
above the surrounding water.
b.
Calculate the maximum number of 75-kg people that
can be on the raft without the top of the raft sinking.
Three objects of identical mass attached to strings are
suspended in a large tank of liquid, as shown.
a.
Some of the liquid is now drained until only half of A is
submerged. Would the tension increase, decrease, or
remain the same? Justify your answer.
4. A 0.025 m3 vessel contains 1 mole of argon gas (M =
0.040 kg/mol) at 400 K. Determine
a. the pressure.
The gas is heated at constant pressure to a volume of
0.055 m3. Determine
b. the work (Win) done during the expansion.
c.
b.
Calculate the speed of the water as it exits from the hole.
c.
Calculate the height h of water needed above the hole
to cause the speed you determined in part (b).
d.
Calculate the distance d from the small hole to the
table top, which would produce a value of x = 0.50 m.
e.
Suppose that there is now less water in the container
so that the height h is reduced to h/2. Where will the
water hit the tabletop?
Calculate the density of the liquid.
6.
d.
Calculate the volume rate of flow of water from the
hole in m3/s.
Must all three strings have the same tension?
The tension in the string supporting A (V = 1.0 x 10-5 m3 and
 = 1300 kg/m3) is 0.0098 N.
b. Calculate the buoyant force on object A.
c.
a.
the change in internal energy of the gas.
The cylinder contains 2.2 kg of water vapor initially at a
volume of 2.0 m3 and an absolute pressure of 3.0 x 105 Pa.
This state is represented by point A in the PV diagram.
a. Calculate the temperature of the water vapor at point A.
The absolute pressure of the water vapor is increased at
constant volume to 4.0 x 105 Pa at point B, and then the
volume of the water vapor is increased at constant
pressure to 2.5 m3 at point C, as shown in the PV diagram.
7.
b.
Calculate the temperature of the water vapor at point C.
c.
Does the internal energy of the water vapor for the
process A  B  C increase, decrease, or remain the
same? Justify your answer.
d.
Calculate the work done on the water vapor for the
process A  B  C.
A 0.03 mol sample of helium is taken through the cycle
shown in the diagram.
a.
Determine the
(1) temperature at point C.
(2) the volume at point C, VC.
b.
Complete the chart.
U
Qin
Win
A B
B C
-800 J
C A
Overall
8.
A 0.20 m diameter cylinder fitted with a frictionless piston,
initially fixed in place. The cylinder contains 2.0 moles of
nitrogen gas at an absolute pressure of 4.0 x 105 Pa.
a. Calculate the force that the nitrogen gas exerts on the
piston.
b.
Calculate the volume of the gas if the temperature of
the gas is 300 K.
c.
In a certain process, the piston is allowed to move,
and the gas expands at constant pressure and pushes
the piston out 0.15 m. Calculate how much work is
done by the gas.
d.
Is heat energy transferred to or from the gas in the
process in part (c)? Justify your answer.