Problems
633
tank is filled with 200 g of water. What is the increase in
the temperature of the water after the blocks fall through
a distance of 3.00 m?
Section 20.2 Specific Heat and Calorimetry
The temperature of a silver bar rises by 10.0°C when it ab-
sorbs 1.23 kJ of energy by heat. The mass of the bar is
525 g. Determine the specific heat of silver.
4. A 50.0-g sample of copper is at 25.0°C. If 1 200 J of energy
is added to it by heat, what is the final temperature of the
copper?
5. Systematic use of solar energy can yield a large saving in
the cost of winter space heating for a typical house in the
north central United States. If the house has good insula-
tion, you may model it as losing energy by heat steadily at
the rate 6 000 W on a day in April when the average exte-
rior temperature is 4°C, and when the conventional heat-
ing system is not used at all. The passive solar energy col-
lector can consist simply of very large windows in a room
facing south. Sunlight shining in during the daytime is ab-
sorbed by the floor, interior walls, and objects in the room,
raising their temperature to 38°C. As the sun goes down,
insulating draperies or shutters are closed over the win-
dows. During the period between 5:00
P
.
M
. and 7:00
A
.
M
.
the temperature of the house will drop, and a sufficiently
large “thermal mass” is required to keep it from dropping
too far. The thermal mass can be a large quantity of stone
(with specific heat 850 J/kg $ °C) in the floor and the inte-
rior walls exposed to sunlight. What mass of stone is re-
quired if the temperature is not to drop below 18°C
overnight?
6. The Nova laser at Lawrence Livermore National Labora-
tory in California is used in studies of initiating controlled
nuclear fusion (Section 45.4). It can deliver a power of
1.60 % 10
13
W over a time interval of 2.50 ns. Compare its
energy output in one such time interval to the energy re-
quired to make a pot of tea by warming 0.800 kg of water
from 20.0°C to 100°C.
A 1.50-kg iron horseshoe initially at 600°C is dropped
into a bucket containing 20.0 kg of water at 25.0°C. What
is the final temperature? (Ignore the heat capacity of the
container, and assume that a negligible amount of water
boils away.)
8.
An aluminum cup of mass 200 g contains 800 g of water
in thermal equilibrium at 80.0°C. The combination of
cup and water is cooled uniformly so that the tempera-
ture decreases by 1.50°C per minute. At what rate is en-
ergy being removed by heat? Express your answer in
watts.
9.
An aluminum calorimeter with a mass of 100 g contains
250 g of water. The calorimeter and water are in thermal
equilibrium at 10.0°C. Two metallic blocks are placed into
the water. One is a 50.0-g piece of copper at 80.0°C. The
other block has a mass of 70.0 g and is originally at a tem-
perature of 100°C. The entire system stabilizes at a final
temperature of 20.0°C. (a) Determine the specific heat of
the unknown sample. (b) Guess the material of the un-
known, using the data in Table 20.1.
7.
3.
10.
A 3.00-g copper penny at 25.0°C drops 50.0 m to the
ground. (a) Assuming that 60.0% of the change in poten-
tial energy of the penny–Earth system goes into increasing
the internal energy of the penny, determine its final tem-
perature. (b) What If ? Does the result depend on the mass
of the penny? Explain.
11.
A combination of 0.250 kg of water at 20.0°C, 0.400 kg of
aluminum at 26.0°C, and 0.100 kg of copper at 100°C is
mixed in an insulated container and allowed to come to
thermal equilibrium. Ignore any energy transfer to or
from the container and determine the final temperature
of the mixture.
12.
If water with a mass m
h
at temperature T
h
is poured into an
aluminum cup of mass m
Al
containing mass m
c
of water at
T
c
, where T
h
(
T
c
, what is the equilibrium temperature of
the system?
13.
A water heater is operated by solar power. If the solar col-
lector has an area of 6.00 m
2
and the intensity delivered by
sunlight is 550 W/m
2
, how long does it take to increase
the temperature of 1.00 m
3
of water from 20.0°C to
60.0°C?
14.
Two thermally insulated vessels are connected by a narrow
tube fitted with a valve that is initially closed. One vessel, of
volume 16.8 L, contains oxygen at a temperature of 300 K
and a pressure of 1.75 atm. The other vessel, of volume
22.4 L, contains oxygen at a temperature of 450 K and a
pressure of 2.25 atm. When the valve is opened, the gases
in the two vessels mix, and the temperature and pressure
become uniform throughout. (a) What is the final temper-
ature? (b) What is the final pressure?
Section 20.3 Latent Heat
15. How much energy is required to change a 40.0-g ice cube
from ice at &10.0°C to steam at 110°C?
16. A 50.0-g copper calorimeter contains 250 g of water at
20.0°C. How much steam must be condensed into the wa-
ter if the final temperature of the system is to reach
50.0°C?
A 3.00-g lead bullet at 30.0°C is fired at a speed of 240 m/s
into a large block of ice at 0°C, in which it becomes em-
bedded. What quantity of ice melts?
18.
Steam at 100°C is added to ice at 0°C. (a) Find the amount
of ice melted and the final temperature when the mass of
steam is 10.0 g and the mass of ice is 50.0 g. (b) What If ?
Repeat when the mass of steam is 1.00 g and the mass of
ice is 50.0 g.
19.
A 1.00-kg block of copper at 20.0°C is dropped into a large
vessel of liquid nitrogen at 77.3 K. How many kilograms of
nitrogen boil away by the time the copper reaches 77.3 K?
(The specific heat of copper is 0.092 0 cal/g $ °C. The la-
tent heat of vaporization of nitrogen is 48.0 cal/g.)
20. Assume that a hailstone at 0°C falls through air at a uni-
form temperature of 0°C and lands on a sidewalk also at
this temperature. From what initial height must the hail-
stone fall in order to entirely melt on impact?
In an insulated vessel, 250 g of ice at 0°C is added to
600 g of water at 18.0°C. (a) What is the final temperature
21.
17.