CHAPTER 9
1 Archimedes Law
The magnitude of the buoyant force always
equals the weight of the fluid displaced by the object
Noste nesteessä on yhtä suuri kuin syrjäytetyn
nestemäärän paino. Hpätee myös kaasuihinL
2 Mass of a stone is 37 kg. Density of the stone is 2.9
a Find the mass of displaced water. ( rw = 1
kg
dm3
kg
dm3
.
)
b Find the buoyant force (noste) on the stone when immersed in water.
(r=
m
V
and
B = rf Vg)
ms = 37; rstone = 2.9; rwater = 1; g = 9.81;
V=
m
rstone
=
37 kg
2.9
= 12.7586 dm3
kg
dm3
mw = rwater V = 1
kg
3
µ 12.7586 dm3 º 12.76 kg
dm
B = rwater µ V µ g º 125 N
Kiven tilavuus = syrjäytetyn veden tilavuus
g = 9.81; r = 2900; m = 37
V=
m
r
=
37 kg
2900
kg
= 0.01276 m3
m3
Noste on syrjäytetyn vesimäärän paino: (Huom: koska m = r V, kaava B = r V g on itse asiassa sama kuin B
= m g, missä m on syrjäytetyn veden massa)
g = 9.81; r = 1000; V = 0.01276 ;
kg
m
B = r V g = 1000
* 0.01276 m3 * 9.81
m3
s2
º 125.2 N
4 Water is to be pumped to the top of the Empire State Building, which is 366 m high. What gauge pressure
(hydrostaattinen paine) is needed in the water line at the base of the building to raise the water to this height?
rwater = 1000; g = 9.81; h = 366; p = rwater g h º 3.59 * 106 Pa
CHAPTER 10
5. A rectangular steel plate with dimensions of 30 cm × 25 cm is heated from 20°C to 220°C. What is its
change in area? (Coefficient of linear expansion for steel is 11 × 10-6 /C°.)
a. 0.82 cm2
b. 1.65 cm2
c. 3.3 cm2
5. A rectangular steel plate with dimensions of 30 cm × 25 cm is heated from 20°C to 220°C. What is its
change in area? (Coefficient of linear expansion for steel is 11 × 10-6 /C°.)
a. 0.82 cm2
b. 1.65 cm2
c. 3.3 cm2
d. 6.6 cm2
DA = 2 a A0 Dt
DA = 2 I11 * 10-6 M H30 * 25L cm2 H220 - 20L º 3.3 cm2
6. What happens to a given mass of water as it is cooled from 4°C to zero?
a. expands
b. contracts
c. vaporizes
d. neither expands, contracts, nor vaporizes
Water exceptionally expands in the interval from 4 °C to 0 °C
7. A 2.00-L container holds half a mole of an ideal gas at a pressure of 12.5 atm. What is the gas temperature? (R = 0.082 1 L atm/mol K or R = 8.31 J/mol K), ideal gas
pV = nRT
a. 1 980 K
b. 1 190 K
c. 965 K
d. 609 K
T=
pV
nR
=
I12.5 µ 1.013 µ 105 M I2 µ 10-3 M
0.5 µ 8.31
= 609.50 K
8 Two moles of nitrogen gas are contained in an enclosed cylinder with a movable piston. If the molecular
m
mass of nitrogen is 28, how many grams of nitrogen are present? In = M M
a. 0.14
b. 56
c. 42
d. 112
m = n * M = 2 mol * 28
g
mol
= 56 g
9 Two moles of nitrogen gas are contained in an enclosed cylinder with a movable piston. If the gas temperature is 298 K, and the pressure is 1.013 × 106 N ë m2 , what is the volume? (R = 8.31 J/mol K)
ideal gas pV = nRT
a. 9.80 × 10-3 m3
b. 4.90 × 10-3 m3
c. 17.3 × 10-3 m3
d. 8.31 × 10-3 m3
pV = nRT
n R T 2 * 8.31 * 298
V=
=
= 0.0048892 m3
6
p
1.013 * 10
10
Two moles of an ideal gas at 3.0 atm and 10°C are heated up to 150 °C. If the volume is held constant
during this heating, what is the final pressure? ideal gas
a. 4.5 atm
b. 1.8 atm
c. 0.14 atm
d. 1.0 atm
p1 V
T1
=
p2 V
T2
10
Two moles of an ideal gas at 3.0 atm and 10°C are heated up to 150 °C. If the volume is held constant
during this heating, what is the final pressure? ideal gas
p1 V
T1
=
p2 V
T2
a. 4.5 atm
b. 1.8 atm
c. 0.14 atm
d. 1.0 atm
p1 V
T1
=
p2 V
T2
p1 = 3; T1 = 10 + 273; T2 = 150 + 273; volume constant Ø it cancels out.
p1
T1
==
p2 =
p2
T2
p1 * T2
T1
º 4.48 atm
11 A steel sphere sits on top of an aluminum ring. The steel sphere (a = 1.10 × 10-5 /C°) has a diameter of
4.0000 cm at 0°C. The aluminum ring (a = 2.40 × 10-5 /C°) has an inside diameter of 3.9940 cm at 0°C.
Closest to which temperature given will the sphere just fall through the ring? (make an equation where final
lenghts are equal: L01
a. 462°C
b. 208°C
c. 116°C
d. 57.7°C
+ a1 L01 Dt = L02 + a2 L02 Dt, Solve Dt.)
ast = 1.1 * 10-5 ; aAl = 2.4 * 10-5 ; dAl = 0.039940; dst = 0.04;
dst + ast * dst * Dt = dAl + aAl * dAl * Dt
0.04 + 4.4 µ 10-7 Dt = 0.03994+ 9.5856 µ 10-7 Dt
Dt º 116 °C
12
9.0 g of water in a 2.0-L pressure vessel is heated to 500°C. What is the pressure inside the container?
(R = 0.082 L atm/mol K, one mole of water has a mass of 18 grams) ideal gas
pV = nRT
a. 7.9 atm
b. 16 atm
c. 24 atm
d. 32 atm
m = 9; V = 2; M = 18; n =
p=
n*R*T
V
m
M
; R = 0.082; T = 500 + 273;
º 15.8 atm º 16 atm
CHAPTER 11
13. A 10-kg piece of aluminum (which has a specific heat of 900 J/kg°C) is warmed so that its temperature
increases by 5.0 C°. How much heat was transferred into it?
heat Iwarming a substanceM Q = m c Dt
a. 4.5 × 104 J
b. 9.0 × 104 J
c. 1.4 × 105 J
d. 2.0 × 105 J
heat Iwarming a substanceM Q = m c Dt
a. 4.5 × 104 J
b. 9.0 × 104 J
c. 1.4 × 105 J
d. 2.0 × 105 J
m = 10; c = 900; Dt = 5;
Q = m c Dt º 45 kJ
14. If one’s hands are being warmed by holding them to one side of a flame, the predominant form of heat
transfer is what process?
a. conduction
b. radiation
c. convection
d. vaporization
b.radiation
15. The use of fiberglass insulation in the outer walls of a building is intended to minimize heat transfer
through what process?
a. conduction
b. radiation
c. convection
d. vaporization
a.conduction
16
How does the heat energy from the sun reach us through the vacuum of space?
a. conduction
b. radiation
c. convection
d. none of the above choices are valid
b. radiation
17. Marc attaches a falling 500-kg object with a rope through a pulley to a paddle wheel shaft. He places the
system in a well insulated tank holding 25 kg of water. When the object falls, it causes the paddle wheel to
rotate and churn the water. If the object falls a vertical distance of 100 m at constant speed, what is the temperature change of the water? (the specific heat of water is 4 186 J/kg °C, and g = 9.81 m ë s2 )
mw * c * Dt ã mobj * h * g;
a. 19 600 C°
b. 4 700 C°
c. 4.7 C°
d. 0.8 C°
mobj = 500; mw = 25; h = 100; g = 9.81; c = 4186;
mw * c * Dt = mobj * h * g;
Dt = 4.69 °C
18. An inventor develops a stationary cycling device by which an individual, while pedaling, can convert
all of the energy expended into heat for warming water. What minimum power must be generated if 300 g
water (enough for 1 cup of coffee) is to be heated in 10 min from 20°C to 95°C? (the specific heat of water is
4 186 J/kg °C)
Equation: m c Dt = Power * time
a. 9 400 W
b. 590 W
c. 160 W
d. 31 W
a. 9 400 W
b. 590 W
c. 160 W
d. 31 W
m = 0.300; t = 600; Dt = 95 - 20; c = 4186;
Q = c * m * Dt;
Q
P=
º 157 W
t
19. A windowpane is half a centimeter thick and has an area of 1.0 m2 . The temperature difference between
the inside and outside surfaces of the pane is 15 C°. What is the rate of heat flow through this window?
(Thermal conductivity for glass is 0.84
heat conduction power P = k A
J
s m °C
).
Th -Tc
L
a. 50 000 J/s (W)
b. 2 500 J/s
c. 1 300 J/s
d. 630 J/s
L = 0.005; A = 1; Dt = 15; k = 0.84;
Dt
P = k*A*
º 2520 W
L
20. A waterfall is 145 m high. What is the increase in water temperature at the bottom of the falls if all the
initial potential energy goes into heating the water? (g = 9.8 m ë s2 , cw = 4 186 J/kg°C)
[ Q = m c Dt = m g h ]
a. 0.16°C
b. 0.34°C
c. 0.69°C
d. 1.04°C
Heat gained by water is equal to relased potential energy of water at 145 m higher IEp = m g hM
cw = 4186; mW cw DT = mW * 9.81 * 145
mW cw DT = mW * 9.81 * 145
mW * 9.81 * 145
DT =
º 0.340 °C
mW c w
21. A solar heating system has a 25.0% conversion efficiency; the solar radiation incident on the panels is 1
000 W ë m2 . What is the increase in temperature of 30.0 kg of water in a 1.00-h period by a 4.00 m2 -area
collector? Hcw = 4 186 J/kg°C)
a. 14.3°C
b. 22.4°C
c. 28.7°C
d. 44.3°C
In one hour the energy collected is, E = 0.25 * 3600 s * 1000
J
s
* 4 = 3 600 000 J
This heats water by : mW cw DT = 3 600 000
30 * 4186 * DT = 3 600 000
DT º 28.7 °C
22. Find the final equilibrium temperature when 10.0 g of milk at 10.0°C is added to 160 g of coffee at
90.0°C. (Assume the specific heats of coffee and milk are the same as water and neglect the heat capacity of
the container.) cwater = 4186 J/kg·ºC
a. 85.3°C
b. 77.7°C
c. 71.4°C
d. 66.7°C
22. Find the final equilibrium temperature when 10.0 g of milk at 10.0°C is added to 160 g of coffee at
90.0°C. (Assume the specific heats of coffee and milk are the same as water and neglect the heat capacity of
the container.) cwater = 4186 J/kg·ºC
a. 85.3°C
b. 77.7°C
c. 71.4°C
d. 66.7°C
Coffee gives heat : mC c H90 - TL; Milk takes heat : mM c HT - 10L;
Assume both have same specific heat c = 4186;
mCoffee = 160; mMilk = 10
mCoffee c H90 - TL = mMilk c HT - 10L
T º 85.3 °C
23. The tungsten filament of a light bulb has an operating temperature of about 2100 K. If the emitting area
of the filament is 1.0 cm2 , and its emissivity is 0.68, what is the power output of the light bulb?
(s = 5.67 × 10-8 W ë m2 K4 ) radiation power P = s A e T4
a. 100 W
b. 75 W
c. 60 W
d. 40 W
T = 2100; A = 1 * 10-4 ; e = 0.68; s = 5.6696 * 10-8 ;
P = s A e T4 º 75 W
CHAPTER 12
24. A system is acted on by its surroundings in such a way that it receives 50 J of heat while simultaneously doing 20 J of work. What is its net change in internal energy?
(DU=Q+W, Q is the heat taken by the system and W is the work done on the system.)
a. 70 J
b. 30 J
c. zero
d. -30 J
Q = 50; W = -20;
DU = Q + W = 30 J
25.
A heat engine exhausts 3 000 J of heat while performing 1 500 J of useful work. What is the efficiency
of the engine? W = Qh - Qc
a. 15%
b. 33%
c. 50%
d. 60%
Qc = 3000; W = 1500;
W
1500
1
eff =
=
= = 33 %
Qh
3000 + 1500 3
26. A heat engine operating between a pair of hot and cold reservoirs with respective temperatures of 500 K
and 200 K will have what maximum efficiency?
(Carnot: ec
a. 60%
b. 50%
c. 40%
d. 30%
=
Th -Tc
)
Th
26. A heat engine operating between a pair of hot and cold reservoirs with respective temperatures of 500 K
and 200 K will have what maximum efficiency?
(Carnot: ec
=
Th -Tc
)
Th
a. 60%
b. 50%
c. 40%
d. 30%
ec =
Th - Tc
Th
=
500 - 200
500
=
3
5
= 60 %, Huom Kelvinit
27.
An engine absorbs 2000 J of heat from a hot reservoir and expels 750 J to a cold reservoir during
each operating cycle. What is the efficiency of the engine? How much work is done during each cycle?
e=
W
Qh
=
2000 - 750
2000
= 62.5 %
W = Qh - Qc = 2000 - 750 = 1250 J