Physics 8: Fluids
A.
Static Fluids (10-1 to 10-7)
1. states of matter
a. solid
1. shape and size unchanged by pressure
2. useful properties are mass and force
b. fluid
1. flows under pressure
2. two phases
a. liquid—incompressible
b. gas—compressible
3. useful properties are density and pressure
a. density,  = m/V (kg/m3)
b. pressure, P = F/A (Pa—Pascal)
c. plasma—ionized atoms at high temperature
2. Pascal's principle
a. pressure applied to a confined fluid is equal to the
pressure throughout the fluid
b. Pin = Pout  Fin/Ain = Fout/Aout
c. Win = Wout  Findin = Foutdout
pressure in a liquid, P = gh
Steps
Algebra
P = Fg/A
start with
substitute mg for Fg
P = mg/A
substitute V for m
P = Vg/A
substitute Ah for V
P = Ahg/A
simplify
P = gh
a. equal in all directions and  to object surface
b. not used with gases because density isn't constant
c. absolute pressure
1. absolute = fluid pressure + air pressure
2. P = gh + Po (Po  1 x 105 Pa = 100 kPa)
4. Archimedes' principle, Fb = fVog
a. the buoyant force (weight loss when an object is
submerged) = weight of displaced fluid (mf = fVo)
1. f = fluid density
2. Vo = object's submerged volume
3.
Steps
Algebra
Fb = F2 – F1 = (P2 – P1)A
start with
substitute gh for P
Fb = (gh2 – gh1)A
regroup
Fb = g(h2 – h1)A
substitute h for h2 – h1
Fb = ghA
substitute V for hA
Fb = fVog
b. partially submerged: Fg = Fb
mog = fVsubg  oVo = fVsub
1. fraction submerged: Vsub/Vo = o/f
2. Fsubmerge = Fb – Fg = fVog – oVog = (f – o)Vog
c. partially supported: Fsupport = Fg – Fb = (o – f)Vog
Fb = Fg – Fsupport = (min air – min fluid)g
d. specific gravity s.g. = object/fluid = mair/(mair – mfluid)
oject = (s.g.)fluid (H2O = 1 g/cm3 = 1000 kg/m3)
Name __________________________
B.
Fluid flow (10-8 to 10-10)
1. streamline—fluid layers slide by each other
2. turbulent—eddy currents (increase viscosity)
3. volume flow rate
V/t = Al/t = Av (m3/s)
assume constant volume when water moves
through closed system, then V/t = A1v1 = A2v2
4. Bernoulli's equation, P + gh + ½v2 = C
a. based on conservation of energy
Steps
Algebra
WP = FPd
start with
substitute PA for Fp
Wp = PAd
l for d
Wp = PAl
Wp = PV
substitute V for Al
Ug = mgh
start with
substitute V for m
Ug = Vgh
K = ½mv2
start with
substitute V for m
K = ½Vv2
total energy is constant PV + Vgh + ½Vv2 = constant
divide both sides by V
P + gh + ½v2 = C
b. three types of problems
1. plumbing system:
a.
b.
C.
P1 + gy1 + ½v12 = P2 + gy2 + ½v22
2. leaking tank (P1 = P2, y2 = 0 and v1 = 0):
gy1 = ½v22  v22 = 2gy1
(same for an object that falls y1 meters!)
3. lift caused by moving air (y1 = y2):
P1 – P2 = ½v22 - ½v22
(F1 – F2)/A = ½(v22 – v12)
Flift = ½(vtop2 – vbottom2)A
Kinetic theory—Gases (13-2, 13-6 to 13-10)
1. temperature scales
a. 2 relative scales: oF, oC
b. 1 absolute scale: K = oC + 273 (use Kelvin
temperature for all calculations except T)
2. molecular kinetic energy
a. per mole: K = 3/2RT = ½Mv2
R = 8.31 J/mol•K
M = mass per mole in kg
b. per molecule: K = 3/2kBT = ½v2
kB = R/6.02 x1023 = 1.38 x 10-23 J/K

 = M/6.02 x 1023
3. ideal gas
a. no cohesive force or appreciable volume
b. PV = nRT = NkBT
P = pressure in Pa (1 x 105 Pa = 1 atm)
V = volume in m3 (1 m3 = 1000 L)
n = moles of molecules
N = number of molecules (N = n x 6.02 x 1023)
T = temperature in K
c. sample of gas: P1V1/T1 = P2V2/T2
D.
E.
Heat (13-3 to 13-4, 14-1 to 14-8)
1. heat, internal energy and temperature
a. internal energy (U) is the sum of bond energy,
energy of position and kinetic energy.
b. temperature (T) is related to the kinetic energy
per mole of molecules (K = 3/2RT)
c. heat (Q) is the transfer of internal energy (U)
from one body to another (we will limit our
discussion to heat transfer from a high
temperature body to a low temperature body)
2. laws governing heat transfer (thermodynamics)
a. If bodies are at the same temperature, there is no
heat transfer between them
b. heat naturally flows from hotter to cooler body until
two bodies reach the same temperature
1. internal energy—U: –Uhot + Ucold = 0
2. entropy—S = Q/T: -Q/Thot + Q/Tcold > 0
c. heat flow, Qin = U + Wout
1. U: change in internal energy
2. Wout: work done as body expands (gases)
3. conservation of energy principle
4. rate of heat flow: H = Qin/t = kA(TH – TL)/L
a. k: thermal conductivity
b. A: exposed surface area
c. TH – TL: outside/inside temperatures
d. L is thickness
5. 2 modes of heat transfer
a. conduction: heat transfer through elastic
collisions from hot atoms to cool atoms
b. radiation: hot molecules emit photons
E = hf (human body glows infrared)
6. convection: fluids move between hot and cold
locations because of pressure/density
differences (convection currents)
3. thermal expansion of solids: L = LoT
4. measuring heat flow
a. liquids and solids (Wout  0)
1. Q = U = mcT
a. specific heat, c, is property of material
(water = 4180 J/kg•K)
b. T can be in oC or K
2, hot object added to cool fluid: |Qhot| = |Qcold|
mhotchot(Thot – Tfinal) = mcoldccold(Tfinal – Tcold)
3. rate of heat transfer: power, P = Q/t
b. monatomic gas
1. constant volume (Wout = 0): Qin = U = 3/2nRT
2. constant pressure (Wout  0)
a. Wout = PV = nRT (only when P = 0)
b. Q = Uin + Wout
Q = 3/2nRT + 2/2nRT = 5/2nRT
Heat Engines (15-1 to 15-2, 15-4 to 15-6)
1. PV diagram (monatomic gas)
a. heating a gas changes pressure and/or volume
b. work is done when volume changes
c. useful formulas:
1. PV = nRT T = PV/nR)
2. U = 3/2nRT = 3/2PV or 3/2PV
3. Win = –PV
4. U = Qin + Win
d. idealized processes on PV diagram for a gas
P
adiabatic (Q = 0)
isometric (V = 0)
isobaric (P = 0)
Po
isothermal (T = 0)
Vo
V
e.
interpretation of graphs
1. move away from origin  +T and +U
2. move toward y-axis (compression)  +Win
3. area under the curve = -Win
f. Summary calculations for each process
Process T (T2 – T1) U
=
Qin
+
Win
3/ PV
Isometric
2
0
PV/nR
= U
3/ nRT
(V = 0)
2
3/ PV
Isobaric
2
PV/nR
U – Win
–PV
3/ nRT
(P = 0)
2
Isothermal
= -Win
= -Qin
0
0
(T = 0)
Adiabatic
= Win
0
= U
(Q = 0)
2. heat cycle 
a. ideal (Carnot) system takes a body of gas through
a complete cycle where U = 0


b. solving heat cycle problems
determine T at each state
determine Qin, Win and U for each process
o isometric, Isobaric, use above formulas
o Isothermal, adiabatic, use given values
o missing values, use:

for any step: U = Qin + Win

for cycle: T = U = 0, Qin – Qout = Wout – Win
c. ideal (Carnot) efficiency: ec = (THigh – TLow)/THigh
d. first law efficiency: e = |Wout – Win|/Qin
Waste = Qin(1 – e)
e. heat engine vs. heat pump
1. heat engine takes in heat to perform work
P
– Area 
Win = QL – QH
2.

V
heat engine expands at TH, contracts at TL
 Win < 0 (work is done by the engine)
heat pump uses work to remove heat
P
+ Area 
Win = QH – QL
V
heat pump expands at TL, contracts at TH
 Win > 0 (work is done to the refrigerator)
b.
Experiments
1.
Specific Gravity Lab
a. Mass a weight in air and submerged in water.
mair (g)
mH2O (g)
Calculate the following from the data.
Formula
Calculation
TFe T = To – Tf
TH2O T = Tf – To
b.
Calculate the following from the data.
Formula
Calculation
s.g. s.g. = mair/(mair – mH2O)
  = s.g.(H2O)
2.
Bernoulli Lab
a. Measure the following distances from the hole in the
plastic bottle.
Distance from the hole to
Distance from hole to the
the table top (dy)
water surface (y1)
b.
Calculate where the water that drains from the hole in
the plastic bottle will land.
Formula
Calculation
3.
Place the 50-mL beaker at the predicted distance dx
from the hole in the plastic bottle so that the water will
land in the beaker. Adjust the position if necessary.
Measure the adjusted distance dx’.
dx
dx’
% Difference
1.
2.
3.
5.
b.
6.
n
n = mMg/24.3
Vm3 Vm3 = (Vo – Vf)10-6
TK TK = ToC + 273
PPa PPa = Plab – PH2O
R
R = PPaVm3/nTK
%  100(8.31 – R)/8.31
4.
4.
Gas Law Constant Lab
a. Mass 0.20 g of Magnesium. Measure the temperature,
pressure and volume of the gas generated when the
magnesium reacts with HCl.
V (mL)
P (Pa)
mMg
T
(g)
(oC)
Vo
Vf
Plab
PH2O
Calculate the following from the data.
Formula
Calculation
Calorimetry lab
a. Mass the iron washers and holder and place in boiling
water for 5 minutes. Add 100 mL of water to a
Styrofoam cup and measure its temperature. Add the
boiling hot steel to the Styrofoam cup of water,
measure the highest temperature,
Iron Washers
Water
m (kg)
To
Tf
m (kg)
To
Tf
100o C
0.100 kg
cFe
QFe = mcT
Practice Problems
dx dx = vxt
c.
QFe = QH2O = mcT
%  100(450 – cFe)/450
t dy = ½gt2
vx gy1 = ½vx2
QFe
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
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
gold (s.g. = 19.3)
lead (s.g. = 11.3)

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)?
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.
What is the volume flow rate in the 4-cm pipe?
c.
What is the velocity of the water in a 2.6-cm diameter
pipe on the second floor of the house.
d, The pressure in the 4-cm pipe is 3 atm. What is the
B. Fluid Flow
pressure in the 2.6 cm section that is elevated 3 m?
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 50. Air ( = 1 kg/m3) passes over a roof at 60 m/s. Determine
artery that is partially blocked. As the platelet moves from the
a. the pressure difference between the attic air and the
wide region into the narrow region, the blood pressure
air passing over the roof.
(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
b. the upward force exerted on the roof (area = 300 m2).
would the results differ if the measurement were made on
the person's leg instead?
(A) higher
(B) same
(C) lower
C. Kinetic Theory—Gases
43. Smoke is drawn up a chimney on a windy day. The draw
51.
Which
is
the
largest
unit, 1o C, 1 K or 1o F?
on a windy day compared to a calm day is
o
(A)
1
C
(B)
1
K
(C) 1oF
(D) 1oC and 1 K
(A) faster
(B) same
(C) slower
o
52. It turns out -40 C is the same temperature as -40o F. Is
44. Consider the diagram in your notes (B3).
there a temperature where the Kelvin and Celsius scales
a. How many times bigger is A1 compared to A2 if the
agree?
diameter, d1, is two times the diameter, d2?
(A) yes 0oC
(B) yes, -273oC
(C) yes, 0 K
(D) no
53. Which has more molecules, one mole of N2 or one mole of
b. How many times faster is v2 compared to v1?
O2?
(A) N2
(B) O2
(C) tie
54. Which weighs more, one mole of N2 or one mole of O2?
45. Consider the water pipe in your notes (B4). What is P2 when
(A) N2
(B) O2
(C) tie
P1 = 3 x 105 Pa, v1 = 2 m/s, v2 = 5 m/s, y1 = 0 m, y2 = 4 m?
55. Two identical cylinders at the same temperature contain
the same gas. If A contains three times as much gas as B,
which cylinder has the higher pressure?
(A) A
(B) B
(C) tie
46. A water leaks out of a hole 5 m below the surface in a tank.
56. Two identical cylinders at the same pressure contain the
same gas. If A contains three times as much gas as B,
a. What is the velocity of water that leaks out of the tank?
which cylinder has the higher temperature?
(A) A
(B) B
(C) tie
57. Two cylinders at the same temperature contain the same
b. What is the radius of the hole in the water tank if the
gas. If A has twice the volume and half the number of
volume rate flow out of the leak is 3 x 10-3 m3/s?
moles as B, how does the pressure of A compare with the
pressure of B?
(A) PA = ¼PB
(B) PA = ½PB
(C) PA = 2PB
47. a. Air flows past the upper surface of an airplane wing at
58. A partially filled, sealed plastic water bottle sits out in the sun,
250 m/s and past the lower surface of the wing at 200
heating the air inside. What happens to the bottle?
m/s. The density of air is 1.0 kg/m3 and the area of
(A) it expands (B) nothing
(C) it shrinks
the wing is 20 m2. What is the net lift on the wing?
59. What happens to the volume of a balloon if you put it in the
refrigerator?
(A) it expands (B) nothing
(C) it shrinks
b. Racing cars have a rear spoiler, which is able to keep
60. In the formulas K = 3/2RT and PV = nRT
the car from lifting up at high speeds. Describe the
a. The value of R is (_________).
design of the spoiler.
b. Why must you use the Kelvin temperature scale for
these calculations?

48. When a truck passes you on the left, your car initially is
pushed right then pulled left. Why?
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?
c.
What is the Kelvin temperature for 25oC?
61. Consider oxygen gas (O2) at 22oC.
a. What is the temperature in Kelvin?
b.
What is the mass of one mole in kg?
c.
What is the mass of one molecule in kg?
d.
What is the average kinetic energy of a molecule?
e.
What is the kinetic energy of a mole?
f.
What is the average speed?
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.
What is the volume (in m3) of one mole of helium
atoms?
d.
What percentage of the total volume (part a) is taken
up by the helium atoms (part c)?
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
e.
What is the volume when the pressure is increased to
2.0 x 105 Pa and the temperature is raised to 44oC?
63. A 0.01 m3 vessel contains 0.02 kg of an ideal gas at 50oC
and a pressure of 3 x 105 Pa. Determine the
a. kinetic energy per molecule
b.
moles of gas are in the vessel (R = 8.31).
c.
molar mass of the gas.
D. Heat
64. Two objects are made of the same material, but have
different masses and temperatures. If the objects are
brought into thermal contact, which one will have the
greatest change in temperature?
(A) the one with the higher initial temperature
(B) the one with the lower initial temperature
(C) the one with the greater mass
(D) the one with smaller mass
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?
(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,
are heated for the same time over the same stove. You
measure the temperatures and find that one liquid has a
higher temperature than the other. Which liquid has a
higher specific heat?
(A) cooler one (B) hotter one (C) tie
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
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
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?

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?
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?
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?
(3) How much heat did the gas absorb?
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?
(4) What is the change in internal energy, U?
c.
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?
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?

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 system?
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.
(3) How much heat did the gas absorb?
(4) What is the change in internal energy, U?
d.

(2) How much work is done to the gas, Win?

(3) What is the change in internal energy, U?
e.
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?
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.
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?
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?

(2) What is the change in internal energy, U?
f.
Graph each change described in parts b-e below.
2 Po
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)
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?
94. An ideal gas undergoes a cyclic process as shown on the
graph of pressure P versus volume V.
Indicate in the chart whether the change is positive (+),
negative (–), unchanged (0), or can't tell (?).
Process
T
U
=
Qin
+
Win
AB
BC
CD

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)
200
DE
EA
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.
b.
The energy supplied to the power plant in 1 hour.
(Hint: electric output = work)
c.
Heat discarded by the power plant.
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.
100
b.
0.01
0.02
What are the temperatures at each point?
V (m3)
A
B
C
96. What is U for an isothermic process?
D
c. Complete the chart by calculating each value.
Step
U
=
Qin
+
Win
AB
BC
CD
DA
Change
d. Why must the change in Qin + Win = 0?
e.
Calculate the area inside the box diagram?
f.
Determine the first law efficiency?
g.
Determine the Carnot efficiency?
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?
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.

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)
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.
100
b.
exhaust heat produced each hour.
c.
exhaust temperature.
50
b.
V (m3)
0.01
0.02
What are the temperatures at each point?
A
B
C
c. Complete the chart.
Step
U
=
Qin
+
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
Win
AB
2.
BC
CA
(D) 5,000
3.
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
4.
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
5.
Each beaker is filled to the same depth with the same
liquid and the area of the flat bottom is the same for each.
Change
d. In which step is work done to the gas?
e.
The density (in kg/m3) of the rock is
(A) 200
(B) 800
(C) 1,250
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?
102. An ideal gas undergoes a cyclic process as shown on the
graph of pressure P versus volume V.
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
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
6.
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
7.
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
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
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.
Questions 9-11 Two pistons are connected in a hydraulic lift. The
19. What is the kinetic energy at 4T?
diameter of the large piston is ten times that of the small.
(A) ¼K
(B) ½K
(C) 2K
(D) 4K
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
20. What is the velocity at 4T?
(A) ¼v
(B) ½v
(C) 2v
(D) 4v
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
21. If wind blows at 30 m/s over your house, the net force on
(C) 500,000 N
(D) 5,000,000 N
the roof (area = 400 m2) is
(A) 100,000 N
(B) 150,000 N
(C) 180,000 N
(D) 200,000 N
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
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
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
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
13. What is the tension when the stone is submerged?
(C) 4.2 x l05 N
(D) 1.125 x l06 N
(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
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
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
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
27. An object floats in water and displaces 150 cm3 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
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
P1 = 500 kPa. In the constriction of the pipe we have
A2 = 2 cm2. The pressure (in kPa) in the constriction is:
(A) 120
(B) 308
(C) 480
(D) 690
29. A T-shaped tube with a constriction is inserted in a vessel
containing a liquid.
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).
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.

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
37. Which process does the most mechanical work on the gas?
(A) 1
(B) 2
(C) 3
(D) all the same
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).
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.
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
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
36. The average rate at which heat is transferred while the
piece of metal is in the liquid is
(A) 4,000 J/s
(B) 4,800 J/s
(C) 6,000 J/s
(D) 9,600 J/s
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.
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
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
45. For which is U negative?
(A) XY
(B) YZ
(C) ZX
(D) Qin and U
2.
b.
the heat gained by the glass container.
c.
the heat lost by the metallic object.
d.
the specific heat of the metallic object.
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
(D) XYZX
water line
Questions 46-47 An ideal gas undergoes the process below.
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.
46. During which process is no work done on or by the gas?
(A) AB
(B) BC
(C) CD
(D) DE

3.
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?
Three objects of identical mass attached to strings are
suspended in a large tank of liquid, as shown.
a.
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.
Calculate the density of the liquid.
d.
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.
(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?

Practice Free Response
1.
Must all three strings have the same tension?
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.
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.
the change in internal energy of the gas.
d
the heat added to the gas.
b.
Calculate the temperature of the water vapor at point C.
the final temperature of the gas.
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.

e.
5.
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.
7.
A 0.03 mol sample of helium is taken through the cycle
shown in the diagram.
a.
a.
b.
Calculate the volume rate of flow of water from the
hole in m3/s.
(2) the volume at point C, VC.
Calculate the speed of the water as it exits from the hole.
b.
c.
d.
Determine the
(1) temperature at point C.
Calculate the height h of water needed above the hole
to cause the speed you determined in part (b).
Complete the chart.
U
Qin
Win
A B
B C
Calculate the distance d from the small hole to the
table top, which would produce a value of x = 0.50 m.
C A
e.
6.
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?
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.
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.