Mastering Physics Solutions Chapter 16 Temperature and Heat
Chapter 16 Temperature and Heat Q.1CQ
Answers to odd-numbered Conceptual Questions can be found in the back of the book A cup of hot coffee is placed on the table Is it ¡n thermal equilibrium? What condition determines when the coffee is in equilibrium?
Solution:
A body is said to be in thermal equilibrium, if there is no exchange of heat between the body and its surroundings
The moment a coffee cup is placed on the table, its temperature is different from that of its surrounding atmosphere. Hence, there is a transformation of heat energy from the coffee cup to the surroundings Therefore, the coffee is not in thermal equilibrium Over time, the temperature of the coffee will decrease until it is the same as the room temperature At this point, it will be in equilibrium, as long as the room stays at the same temperature
Chapter 16 Temperature and Heat Q.1P
The official record for the lowest temperature ever recorded on Earth was set at Vostok, Antarctica, on July 21, 1983. The temperature on that day fell to —89.2°C, well below the temperature of dry ice. What is this temperaturein degrees Fahrenheit?
Solution:
Chapter 16 Temperature and Heat Q.2CQ
Answers to odd-numbered Conceptual Questions can be found in the back of the book To find the temperature at the core of the Sun. you consult some Web sites on the Internet
One site says the temperature is about 15 million °C. another says it is 15 million kelvin. Is this a serious discrepancy? EXplain.
Solution:
Chapter 16 Temperature and Heat Q.2P
More than likely, there is a glowing incandescent lightbulb in your room at this moment. The filament of that bulb, with a temperature of about 4500 °F, is almost half as hot as the surface of the Sun. What is this temperature in degrees Celsius?
Solution:
Chapter 16 Temperature and Heat Q.3CQ
Answers to odd-numbered Conceptual Questions can be found in the back of the book.
To find the temperature at the core of the Sun, you consult some Web sites on the Internet. One site says the temperature is about 15 million °C, another says it is 15 million kelvin. Is this a serious discrepancy? Explain.
Solution:
Chapter 16 Temperature and Heat Q.3P
Nonnalbody temperature for humans is 98.6°F. What is the corresponding temperature in (a) degrees Celsius and (b) kelvins?
Solution:
Chapter 16 Temperature and Heat Q.4CQ
Answers to odd-numbered Conceptual Questions can be found in the back of the book Is It valid to say that a hot object contains more heat than a cold object?
Solution:
Heat is not a quantity that one object has more of than another. Heat is the energy that is transferred between objects of different temperatures
Chapter 16 Temperature and Heat Q.4P
Whai is the temperature 1.0 K on the Fahrenheit scale?
Solution:
Chapter 16 Temperature and Heat Q.5CQ
Answers to odd-numbered Conceptual Questions can be found in the back of the book. If the glass in a glass thermometer had the same coefficient of volume expansion as mercury the thermometer would not be very useful. Explain.
Solution:
If the glass and the mercury had the same coefficient of volume expansion, the level of mercury in the glass would not change with temperature. This is because the volume of the cavity in the glass would expand by the same amount as the volume of mercury.
Chapter 16 Temperature and Heat Q.5P
The temperature at tire surface of the Sun is about 6000 K. Convert this temperature to the (a) Celsius and (b) Fahrenheit scales.
Solution:
Chapter 16 Temperature and Heat Q.6CQ
Answers to odd-numbered Conceptual Questions can be found in the back of the book Suppose the glass in a glass thermometer expands more with temperature than the mercury it holds What would happen to the mercury level as the temperature increased?
If the glass of the glass thermometer expands faster than mercury with temperature. then it will appear that the mercury is moving downwards with respect to the markings on the thermometer
Solution:
Hence, the temperature shown by the thermometer will decrease with increasing temperature.
Chapter 16 Temperature and Heat Q.6P
One day you notice that the outside temperature increased by 27 F° between your early morning jog and your lunch at noon. What is the corresponding change in temperature in the (a) Celsius and (b) Kelvin scales?
Solution:
Chapter 16 Temperature and Heat Q.7CQ
Answers to odd-numbered Conceptual Questions can be found in the back of the book When a mercury-in-glass thermometer is inserted into a hot liquid the mercury column first drops and then rises. Explain this behavior.
Solution:
The mercury levels drop at the beginning because the glass is the first to increase its temperature when it comes into contact with the hot liquid Therefore, the glass expands before the mercury. leading to a drop in leveli As the mercury rises to the same temperature a few moments later, its level will increase
Chapter 16 Temperature and Heat Q.7P
Tine gas in a constant-volume gas thermometer has a pressure of 93.5 kPa at 105 °C (a) What is the pressure of the gas at 50.0 °C? (b) At what temperature does the gas have a pressure of 115 kPa?
Solution:
Chapter 16 Temperature and Heat Q.8CQ
Answers to odd-numbered Conceptual Questions can be found in the back of the book Sometimes the metal lid on a glass jar has been screwed on so tightly that it is very difficult to open Explain why holding the lid under hot running water often loosens it enough for easy opening
Solution:
Heating the glass jar and its metal lid to the same higher temperature results in a greater expansion in the lid than in the glass I As a result, the lid becomes loose enough to turn.
Chapter 16 Temperature and Heat Q.8P
A constant-volume gas thermometer has a pressure of 80.3 kPa at -10.0 °C and a pressure of 86.4 kPa at 10.0 °C. (a) At what temperature does the pressure of this system extrapolate to zero? (b) What are the pressures of the gas at the freezing and boiling points of water? (c) In general terms, how would your answers to parts (a) and (b) change if a different constant-volume gas thermometer is used? Explain.
Solution:
Chapter 16 Temperature and Heat Q.9CQ
Answers to odd-numbered Conceptual Questions can be found in the back of the book. Why do you hear creaking and groaning sounds in a house. particularly at night as the air temperature drops?
Solution:
As the temperature of the house decreases, the length of the various pieces of wood from which it is constructed will decrease as well s the house adjusts to these changing lengths. it will often creak or groan
Chapter 16 Temperature and Heat Q.9P
A world record for the greatestchange in temperature was set in Spearfish, SD, on January 22, 1943. At 7:30 a.m. the temperature was −4.0 °F; two minutes later the temperature was 45 °F. Find the average rate of temperaturechange during those two minutes in kelvins per second.
Solution:
Chapter 16 Temperature and Heat Q.10CQ
Answers to odd-numbered Conceptual Questions can be found in the back of the book Two different objects receive different amounts of heat but experience the same increase in temperature. Give at least two possible reasons for this behavior
Solution:
Chapter 16 Temperature and Heat Q.10P
We know that −40°C corresponds to −40 °F. What temperature has the same value in both the Fahrenheit and Kelvin scales?
Solution:
Chapter 16 Temperature and Heat Q.11CQ
Answers to odd-numbered Conceptual Questions can be found in the back of the book The specific heat of concrete is greater than that of soil Given this fact, would you expect a
major-league baseball field or the parking lot that surrounds it to cool off more in the evening following a sunny day?
Solution:
The soil in the field cools off faster than the concrete parking lot because its temperature changes more for a given amount of heat loss
Chapter 16 Temperature and Heat Q.11P
When the bulb of a constant-volume gas thermometer is placed in a beaker of boiling water at 100 °C, the pressure of the gas is 227 mmHg. When the bulb is moved to an ice-salt mixture, the pressure of the gas drops to 162 mmHg. Assuming ideal behavior, as in Figure 16-3, what is the Celsius temperature of the ice-salt mixture?
Solution:
Chapter 16 Temperature and Heat Q.12CQ
Answers to odd-numbered Conceptual Questions can be found in the back of the book The specific heat of concrete is greater than that of soil Given this fact, would you expect a major-league baseball field or the parking lot that surrounds it to cool off more in the evening following a sunny day?
Solution:
The soil in the field cools off faster than the concrete parking lot because its temperature changes more for a given amount of heat loss
Chapter 16 Temperature and Heat Q.12P
Bimetallic strip A is made of copper and steel: bimetallic strip B is made of aluminum and steel. (a) Referring to Table 16-1. which strip bends more for a given change in temperature? (b) Which of the metals listed in Table 16-1 would give the greatest amount of bend when combined with steel in a bimetallic strip?
Solution:
(A) The amount of bend in a bimetallic strip depends on the difference in the coefficients of thermal expansion. lEor the two metals, the greater the difference in thermal expansion. the greater the bend This is why strip 2 (aluminum-steel) bends more than strip I (copper-steel)
(B) IThe steel-lead bimetallic strip would give the greatest amount of bend for the metal in the table
Chapter 16 Temperature and Heat Q.13CQ
Answers to odd-numbered Conceptual Questions can be found in the back of the book Extending the result of the previous question to a larger scale, would you expect daytime winds to generally blow from a city to the surrounding suburbs or from the suburbs to the city? Explain
Solution:
The soil in the field cools off faster than the concrete packing because its temperature changes more for a given amount of heat loss If the temperature is extended to the large scale, the ground warms up during the day. Hence. the ground of the surrounding suburbs warms up faster since it has a smaller specific heat. This would lead to a blowing from the city to the suburbs, if the city is warmer than the suburbs because of factories and vehicles the wind would blow in to the city instead. Yes. The day time winds blow from a city to the surrounding suburbs.
Chapter 16 Temperature and Heat Q.13P
Referring to Table 16-1. which would be more accurate for all-season outdoor use: a tape measure made of steel or one made of aluminum?
Solution:
The steel tape measure would be better because its coefficient of thermal expansion is smaller than the aluminum tape measurel This means that its length would change less with temperature
Chapter 16 Temperature and Heat Q.14CQ
Answers to odd-numbered Conceptual Questions can be found in the back of the book When you touch a piece of metal and a piece of wood that are both at room temperature the metal feels cooler Why?
Solution:
Both the metal and the wood are at a lower temperature than your skin. Therefore, heat will flow from your skin to both the metal and the wood. IThe metal feels cooler, however. because it has
greater thermal conductiviN. This allows the heat from your skin to flow to a larger effective volume than in the case of the wood.
Chapter 16 Temperature and Heat Q.14P
A brass plate has a circular hole whose diameter is slightly smaller than the diameter of an
aluminum ball. If the ball and the plate are always kept at the same temperature. (a) should the
temperature of the system be increased or decreased in order for the ball to fit through the
hole? (b) Choose the best explanation from among the following:
L The aluminum ball changes its diameter more with temperature than the brass plate, and
therefore the temperature should be decreased.
IL Changing the temperature won’t change the fact that the ball is larger than the hole.
IlL Heating the brass plate makes its hole larger, and that will allow the ball to pass through.
Solution:
Explain whether the temperature of the system be increased or decreased in order for the aluminum balito fit through the hole of the brass piate This can be explained basing on the concept of coefficient of thermal expansion Given that the diameter of the hole is slightly smaller than the diameter of the ball The aluminum ball and the hole of the brass plate are kept at same temperature From Table 16-1
shown in the textbook the value of coefficient of linear expansion of aluminum is more compared to the value of coefficient of linear expansion of brass To fit the ball through the hole the
system should be cooled. This is because inWally the diameter of the ball is slightly larger than the diameter of the hole and if the system is cooled the ball will contract by a greater amount than compared to that of the hole and hence the ball lits through the hola Thus, the temperature of the system should be decreased for the ball to fit through the hola Given that the diameter of the hole is slightly smaller than the diameter of the ball The aluminum ball and the hole of the brass plate are kept at same temperatura From Table 16-1 shown in the textbook the value of coefficient of linear expansion of aluminum is more compared to the value of coefficient of linear expansion of brass. So if the temperature is decreased the diameter of the aluminum ball changes more compared to that of the hole.
If the temperature is changed (increased) then the ball will expand more compared to the hola Heating the system. results that the aluminum ball will expand at a faster rate than the hole of
the brass plata Hence, the correct statement is (l)
Chapter 16 Temperature and Heat Q.15CQ
Answers to odd-numbered Conceptual Questions can be found in the back of the book. After lighting a wooden match, you can hold onto the end of it for some time, until the flame almost rthees your lingers. Why aren’t you burned as soon as the match is lit?
Solution:
Even though the flame at the far end of the match is very hot, the wood from which it is made is a poor conductor of heat. rrhe air between the flame and finger is an even poorer conductor of heat. Thus we are not burned as soon as the match is lit
Chapter 16 Temperature and Heat Q.15P
Solution:
Chapter 16 Temperature and Heat Q.16CQ
Answers to odd-numbered Conceptual Questions can be found in the back of the book.
The rate of heat flow through a slab does not depend on which of the following? (a) The temperature difference between opposite faces of the slab, (b) The thermal conductivity of the slab. (c) The thickness of the slab, (d) The cross-sectional area of the slab, (e) The specific heat of the slab.
Solution:
Chapter 16 Temperature and Heat Q.16P
Referring to Problem 15, rank the metal plates in order of increasing expansion in area. Indicate ties where appropriate.
Solution:
Chapter 16 Temperature and Heat Q.17CQ
Answers to odd-numbered Conceptual Questions can be found in the back of the book. If a lighted match is held beneath a balloon inflated with air, the balloon quickly bursts If.
instead, the lighted match is held beneath a balloon tilled with water, the balloon remains intact. even il the llame comes in contact with the balloon Explain
Solution:
Two important factors work in favor of the water filled balloon.
(i) rI’he water has a larger heat capacity; hence it can take on a large amount of he at with a little change in temperature.
(ii) [Water is a better conductor of heat than airj; henc e the heat from the flame is conducted into a large volume of water-which gives larger effective heat capacity.
Chapter 16 Temperature and Heat Q.17P
The world’s longest suspension bridge is the Akashi Kaikyo Bridge in Japan. The bridge is 3910 m long and is constructed of steel. How much longer is the bridge on a warm summer day (30.0 °C) than on a cold winter day (−5.00 °C)?
Solution:
Chapter 16 Temperature and Heat Q.18CQ
Answers to odd-numbered Conceptual Questions can be found in the back of the book Upclrafts of air allow hawks and eagles to glide effortlessly, all the while gaining altitude What causes the upclrafts?
Solution:
Updraft of air is due to warm air on the surface of earth On daytime heating of surface of earth causes surface air to become much warmer than the air above the surface of earth The density of warm air is much smaller than that of density of cool air The warm air on surface is raises up from the surface of earth due to less density Therefore. warm air on the surface causes upright of airl.
Chapter 16 Temperature and Heat Q.18P
A hole in an aluminum plate has a diameter of 1.178 cm at 23.00 °C, (a) What is the diameter of the hole at 199.0 °C? (b) At what temperature is the diameter of the hole equal to 1.176 cm?
Solution:
Chapter 16 Temperature and Heat Q.19CQ
Answers to odd-numbered Conceptual Questions can be found in the back of the book When penguins huddle together during an Antarctic storm, they are warmer than if they are well separated Explain
Solution:
When there is one penguin in a given area, heat is radiated from the penguin to the entire area But when there are a group of penguins, the heat radiated by all penguins goes into the same area So the heat radiated per area ¡s more in the case of the group of penguins, rather than a single penguin
Chapter 16 Temperature and Heat Q.19P
Solution:
Chapter 16 Temperature and Heat Q.20CQ
Answers to odd-numbered Conceptual Questions can be found in the back of the book Thefur of polar bears consists of hollow fibers (Sometimes algae will grow inthe hollow regions. giving tine fur a green cast.) Explain why hollow hairs can be beneficial to the polar bears.
Solution:
The hollow fibers of hair are effective insulators because the gas within the fibers has low thermal conductivit This is analogous to double-pane windows, which trap a layer of gas between the panes for a greatly-enhanced insulating effect.
Chapter 16 Temperature and Heat Q.20P
At 12.25 °C a brass sleeve has an inside diameter of 2.19625 cm and a steel shaft has a diameter of 2.19893 cm. It is desired to shrink-fit the sleeve over the steel shaft, (a) To what temperature must the sleeve be heated in order for it to slip over the shaft? (b) Alternatively, to what temperature must the shaft be cooled before it is able to slip through the sleeve?
Solution:
Chapter 16 Temperature and Heat Q.21CQ
Answers to odd-numbered Conceptual Questions can be found in the back of the book Object 2 has twice the emissivity of object 1. though they have the same size and shape If the two objects radiate the same power. what is the ratio of their Kelvin temperatures?
Solution:
Obiect 1 must have the higher temperaturel to compensate for object 2s greater emissivity Since the radiated power depends on temperature4, the temperature of object 1 must be greater by a factor of 2 to the 114th power.
Chapter 16 Temperature and Heat Q.21P
Early in the morning, when the temperature is 5.0 °C, gasoline is pumped into a car’s 51-L steel gas tank until it is filled to the top. Later in the day the temperature rises to 25°C. Since the volume of gasoline increases more for a given temperature increase than the volume of the steel tank, gasoline will spill out of the tank. Mow much gasoline spills out in this case?
Solution:
Chapter 16 Temperature and Heat Q.22P
Some cookware has a stainless steel interior (α = 17.3 × 10−6 K− 1) and a copper bottom (α = 17.0 × 10−6 K−1) for better heat distribution. Suppose an 8.0 in. pot of this construction is heated to 610 °C on the stove. If the initial temperature of the pot is 22 °C, what is the difference in diameter change for the copper and the steel?
Solution:
Chapter 16 Temperature and Heat Q.23P
You construct two wire-frame cubes, one using copper wire, the other using aluminum wire. At 23 °C the cubes enclose equal volumes of 0.016 m3. (a) If the temperature of the cubes is increased, which cube encloses the greater volume? (b) Find the difference in volume between the cubes when their temperature is 97 °C.
Solution:
Chapter 16 Temperature and Heat Q.24P
A copper ball with a radius of 1.5 cm is heated until its diameter has increased by 0.19 mm. Assuming an initial temperature of 22 °C, find the final temperature of the ball.
Solution:
Chapter 16 Temperature and Heat Q.25P
An aluminum saucepan with a diameter of 23 cm and a height of 6.0 cm is filled to the brim with water. The initial temperature of the pan and water is 19 °C. The pan is now placed on a stove burner and heated to 88 °C. (a) Will water overflow from the pan, or willthe water level in the pan decrease? Explain, (b) Calculate the volume of water that overflows or the drop in water level in the pan, whichever is appropriate.
Solution:
Chapter 16 Temperature and Heat Q.26P
When people sleep, their metabolic rate is about 2.6 × 10 −4 C/(s kg). How many Calories docs a 75-kg person metabolize while getting a good night’s sleep of 8.0 hr?
Solution:
Chapter 16 Temperature and Heat Q.27P
An exercise machine indicates that you have worked off 2.5 Calories in a minute-and-a-half of running in place. What was your power output during this time? Give your answer in both watts and horsepower.
Solution:
Chapter 16 Temperature and Heat Q.28P
During a workout, a person repeatedly lifts a 12-1 b barbell through a distance of 1.3 ft. How many “reps” of this lift are required to burn off 150 C?
Solution:
Chapter 16 Temperature and Heat Q.29P
Consider the apparatus tha t Joule used in his experiments on the mechanical equivalent of heat, shown in Figure16-8. Suppose both blocks have a mass of 0.95 kg and that they fall through a distance of 0.48 m. (a) Find the expected rise in temperature of the water, given that 6200 J are needed for every 1.0 C° increase. Give your answer in Celsius degrees, (b) Would the temperature rise in Fahrenheit degrees be greater than or less than the result in part (a)? Explain, (c) Find the rise in temperature in Fahrenheit degrees.
Solution:
Chapter 16 Temperature and Heat Q.30P
It was shown in Example that atypical person radiates about 62 W of power at room temperature. Given this result, how long does it take for a person to radiate away the energy acquired by consuming a 230-Calorie doughnut?
Solution:
Chapter 16 Temperature and Heat Q.31P
Two objects are made of the same material but have different temperatures, Object 1 has a mass m and object 2 has a mass 2m. If the objects are brought into thermal contact, (a) is the temperature change of object 1 greater than, less than, or equal to the tempera ture change of object 2? (b) Choose the best explanation from among the following:
I. The larger object gives up more heat, and therefore its temperature change is greatest
II. The heat given up by one object is taken up by the other object. Since the objects have the same heat capacity, the temperature changes are the same.
III. One object loses heat of magnitude Q, the other gains heat of magnitude Q. With the same magnitude of heat involved, the smaller object has the greater temperature change.
Solution:
Chapter 16 Temperature and Heat Q.32P
A certain amount of heat is transferred to 2 kg of aluminum, and the same amount of heat is transferred to 1 kg of ice. Referring to Table 16-2, (a) is the increase in temperature of the aluminum greater than, less than, or equal to the increase in temperature of the ice? (b) Choose the best explanation from among the following:
I. Twice the specific heat of aluminum is less than the specific heat of ice, and hence the aluminum has the greater temperature change.
II. The aluminum has the smaller temperature change since its mass is less than that of the ice.
III. The same heat will cause the same change in temperature.
Solution:
Chapter 16 Temperature and Heat Q.33P
Suppose 79.3 J of heat are added to a 111-g piece of aluminum at 22.5 °C. What is the final temperature of the aluminum?
Solution:
Chapter 16 Temperature and Heat Q.34P
How much heat is required to raise the temperature of a 55-g glass ball by 15 C°?
Solution:
Chapter 16 Temperature and Heat Q.35P
Estimate the heat required to heat a 0.15-kg apple from 12 °C to 36 °C. (Assume the apple is mostly water.)
Solution:
Chapter 16 Temperature and Heat Q.36P
A 5.0-g lead bullet is fired into a fence post. The initial speed of the bullet is 250 m/s, and when it comes to rest, half its kinetic energy goes into hearing the bullet. How much does the bullet’s temperature increase?
Solution:
Chapter 16 Temperature and Heat Q.37P
Silver pellets with a mass of 1.0 g and a temperature of 85 °C are added to 220 g of water at 14 °C (a) How many pellets must be added to increase the equilibrium temperature of the system to 25 °C? Assume no heat is exchanged with the surroundings, (b) If copper pellets are used instead, does the required numberof pellets increase, decrease, or stay the same? Explain, (c) Find the number of copper pellets that are required.
Solution:
Chapter 16 Temperature and Heat Q.38P
A 235-g lead ball at a temperature of 84.2 °C is placed in a light calorimeter containing 177 g of water at 21.5 °C Find the equilibrium temperature of the system.
Solution:
Chapter 16 Temperature and Heat Q.39P
If 2200 J of heat are added to a 190-g object, its temperature increases by 12 C°. (a) What is the heat capacity of this object? (b) What is the object’s specific heat?
Solution:
Chapter 16 Temperature and Heat Q.40P
An 97.6-g lead ball is dropped from rest from a height of 4.57 m. The collision between the ball and the ground is totally inelastic. Assuming all the ball’s kinetic energy goes into heating the ball, find its change in temperature.
Solution:
Chapter 16 Temperature and Heat Q.41P
To determine the specific heat of an object, a student heats it to 100 °C in boiling water. She then places the 38.0-g object in a 155-g aluminum calorimeter containing 103 g of water. The aluminum and water are initially at a temperature of 20.0 °C, and are thermally insulated from their surroundings. If the final temperature is 22.0 °C, what is the specific heat of the object? Referring to Table 16-2, identify the material in the object.
Solution:
Chapter 16 Temperature and Heat Q.42P
At the local county fair, you watch as a blacksmith drops a 0.50-kg iron horseshoe into a bucket containing 25 kg of water, (a) If the initial temperature of the horseshoe is 450 °C, and the initial temperature of the water is 23 °C, what is the equilibrium temperature of the system? Assume no heat is exchanged with the surroundings, (b) Suppose the 0.50-kg iron horseshoe had been a 1.0-kg lead horseshoe instead. Would the equilibrium temperature in this case be greater than, less than, or the same as in part (a)? Explain.
Solution:
Chapter 16 Temperature and Heat Q.43P
Solution:
Chapter 16 Temperature and Heat Q.44P
In a popular lecture demonstration, a sheet of paper is wrapped around a rod that is made from wood on one half and metal on the other half, 1 f held over a flame, the paper on one half of the rod is burned while the paper on the other half is unaffected, (a) Is the burned paper on the wooden half of the rod, or on the metal half of the rod? (b) Choose the best explanation from among the following:
I. The metal will be hotter to the touch than the wood; therefore the metal side will be burnt.
II. The metal conducts heat better than the wood, and hence the paper on the metal half is unaffected.
III. The metal has the smaller specific heat; hence it heats up more and burns the paper on its half of the rod.
Solution:
Charge carriers can flow easily in a conductor, but in an insulator there is no flow of charge carriers.
In this case iron is the conductor, and wood is the insulator.
(a)
The burned paper is on the wooden half of the rod.(b)The best explanation is as follows:
II. The metal conducts heat better than the wood, and hence the paper on the metal half is unaffected.
Chapter 16 Temperature and Heat Q.45P
Solution:
Chapter 16 Temperature and Heat Q.46P
Solution:
Chapter 16 Temperature and Heat Q.47P
On a sunny day identical twins wear different shirts. Twin 1 wears a dark shirt; twin 2 wears a light-colored shirt. Which twin has the warmer shirt?
Solution:
Chapter 16 Temperature and Heat Q.48P
Two bowls of soup with identical temperatures areplaced on a table. Bowl 1 has a metal spoon in it; bowl 2 does not. After a few minutes, is the temperature of the soup in bowl 1 greater than, less than, or equal to the temperature of the soup in bowl 2?
Solution:
The temperature in bowl 1 is less than the temperature in bowl 2. This is because in bowl 1, heat is conducted not only to the surrounding air, but also to the spoon. However, for bowl 2, heat is conducted only to the surrounding air.
Chapter 16 Temperature and Heat Q.49P
A glass window 0.35 cm thick measures 84 cm by 36 cm. How much heat flows through this window per minute if the inside and outside temperatures differ by 15 C°?
Solution:
Chapter 16 Temperature and Heat Q.50P
To compare the relative efficiency of air and glass as insulators, repeat the previous problem with a 0.35-cm-thick layer of air instead of glass. By what factor is the rate of heat transfer reduced?
Solution:
The rate of heat transfer is directly proportional to the area of cross section, temperature difference and inversely proportional to the length.
The rate of heat transfer through glass is given as follows:
Chapter 16 Temperature and Heat Q.51P
Assuming your skin temperature is 37.2 °C and the temperature of your surroundings is 21.8 °C, determine the length of time required for you to radiate away the energy gained by earing a 306-Calorie ice cream cone. Let the emissivity of your skin be 0.915 and its area be 1.22 m2.
Solution:
Chapter 16 Temperature and Heat Q.52P
Find the heat that flows in 1.0 s through a lead brick 15 cm long if the temperature difference between the ends of the brick is 9.5 C°. The cross-sectional area of the brick is 14 cm2.
Solution:
Chapter 16 Temperature and Heat Q.53P
Consider a double-paned window consisting of two panes of glass, the with a thickness of 0.500 cm and an area of 0.725 m2, separated by a layer of air with a thickness of 1.75 cm. The temperature on one side of the window is 0.00 °C; the temperature on the other side is 20.0 °C. In addition, note that the thermal conductivity of glass is roughly 36 times greater than that of air. (a) Approximate the heat transfer through this window by ignoring the glass. That is, calculate the heat flow per ; second through 1.75 cm of air with a temperature difference of 20.0 C°. (The exact result for the complete window is 19.1 J/s.) (b) Use the approximate heat flow found in part (a) to find an approximate temperature difference across the pane of glass. (The exact result is 0.157 C°.)
Solution:
Chapter 16 Temperature and Heat Q.54P
Two metal rods of equal length—one aluminum, the other stainless steel—are connected in parallel with a temperatureof 20.0 °C at one end and 118 °C at the other end. Both rods have a circular cross section with a diameter of 3.50 cm. (a) Determine the length the rods must have if the combined rate of heat flow through them is to be 27.5 J per second, (b) If the length of the rods is doubled, by what factor does the rate of heat flow change?
Solution:
Chapter 16 Temperature and Heat Q.55P
Two cylindrical metal rods—one copper, the other lead—are connected in parallel with a temperature of 210 °C at one end and 112 °Cat the other end. Both rods are 0.650 m in length, and the lead rod is 2.76 cm in diameter. If the combined rate of heat Sow through the two rods is 33.2 J/s, what is the diameter of the copper rod?
Solution:
Chapter 16 Temperature and Heat Q.56P
Solution:
Chapter 16 Temperature and Heat Q.57P
Consider two cylindrical metal rods with equal cross section—one lead, the other aluminum—connected in series. The temperature at the lead end of the rods is 20.0 °C; the temperature at the aluminum end is 80.0 °C. (a) Given that the temperature at the lead-aluminum interface is 50.0 °C, and that the lead rod is 14 cm long, what condition can you use to find the length of the aluminum rod? (b) Find the length of the aluminum rod.
Solution:
Chapter 16 Temperature and Heat Q.58P
A copper rod 81 cm long is used to poke a fire. The hot end of the rod is maintained at 105 °C and the cool end has a constant temperature of 21 °C. What is the temperature of the rod 25 cm from the cool end?
Solution:
Chapter 16 Temperature and Heat Q.59P
Two identical objects are placed in a room at 21 °C. Object 1 has a temperature of 98 °C, and object 2 has a temperatureof 23 °C. What is the ratio of the net power emitted by object 1 to that radiated by object 2?
Solution:
Chapter 16 Temperature and Heat Q.60P
A block has the dimensions L, 21, and 3L. When one of the L × 2L faces is maintained at the temperature T 1 and the other L × 2L face is held at the temperature T 2, the rate of heat conduction throughthe block is P. Answer the following questions in terms of P. (a) What is the rate of heat conduction in this block if one of the L × 3L faces is held at the temperature T 1 and the other L × 3L face is held at the temperature T 2? (b) What is the rate of heat conduction in this block if one of the 2L × 3L faces is held at the temperature T 1 and the other 2L × 3L face is held at the temperature T 2?
Solution:
Chapter 16 Temperature and Heat Q.61GP
Asteel tape measure is marked in such a way thatitgives accurate length measurements at a normal room temperature of 20 °C. If this tape measure is used outdoors on a cold day when the temperature is 0°C, are its measurements too long, too short, or accurate?
Solution:
The measurements on a cold day are too long because the steel tape contracts due the decreased temperature. When we measure the length with the second tape on a cold day, it shows a larger measurement. Thus, the distance between the tick marks on the tape measure have decreased. Therefore, the cool tape measures show more tick marks between the two points than they should.
Chapter 16 Temperature and Heat Q.62GP
A pendulum, is made from an aluminum rod with a mass attached to its free end. if the pendulum is cooled, (a) does the pendulum’s period increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
I. The period of a pendulum depends only on its length and the acceleration of gravity. It is independent of mass and temperature.
II. Cooling makes everything move more slowly, and hence the period of the pendulum increases.
III. Cooling shortens the aluminum rod, which decreases the period of the pendulum.
Solution:
Chapter 16 Temperature and Heat Q.63GP
Solution:
Chapter 16 Temperature and Heat Q.64GP
Referring to the copper ring in the previous problem, imagine that initially the ring is hotter than room temperature, and that an aluminumrod that is colder than room temperature fits snugly inside the ring. When this system rthees thermal equilibrium at room temperature, is the rod (A, firmly wedged in the ring; or B, can it be removed easily)?
Solution:
Chapter 16 Temperature and Heat Q.65GP
The specific heat of alcohol is about half that of water. Suppose you have 0.5 kg of alcohol at the temperature 20 °C in one container, and 0.5 kg of water at the temperature 30 °C in a second container. When these fluids are poured into the same container and allowed to come to thermal equilibrium, (a) is the final temperature greater than, less than, or equal to 25 °C? (b) Choose the best explanation from among the following:
I. The low specific heat of alcohol pulls in more heat, giving a final temperature that is less than 25°.
II. More heat is required to change the temperature of water than to change the temperature of alcohol. Therefore, the final temperature will be greater than 25°.
III. Equal masses are mixed together; therefore, the final temperature will be 25°, the average of the two initial temperatures.
Solution:
Chapter 16 Temperature and Heat Q.66GP
Hot tea is poured from the same pot into two identical mugs. Mug 1 is filled to the brim; mug 2 is filled only halfway. Is the rate of cooling of mug 1 (A, greater than; B, less than; or C, equal to) the rate of cooling of mug 2?
Solution:
Chapter 16 Temperature and Heat Q.67GP
Making Steel Sheets In the continuous-caster process, steel sheets 25.4 cm thick, 2.03 m wide, and 10.0 m long are produced at a temperature of 872 °C. What are the dimensions of a steel sheet once it has cooled to 20.0 °C?
Solution:
Chapter 16 Temperature and Heat Q.68GP
The Coldest Place in the Universe The Boomerang nebula holds the distinction of having the lowest recorded temperature in the universe, a frigid −272 °C. What is this temperature in kelvins?
Solution:
Chapter 16 Temperature and Heat Q.69GP
When technicians work on a computer, they often ground themselves to prevent generating a spark. If an electrostatic discharge does occur, it can cause temperatures as high as 1500 °C in a localized area of a circuit. Temperatures this high can melt aluminum, copper, and silicon. What is this temperature in (a) degrees Fahrenheit and (b) kelvins?
Solution:
Chapter 16 Temperature and Heat Q.70GP
Two objects at the same initial temperature absorb equal amounts of heat. 1 f the final temperature of the objects is different, it may be because they differ in which of the following
properties: mass; coefficient of expansion; thermal conductivity; specific heal?
Solution:
Chapter 16 Temperature and Heat Q.71GP
From the surreal realm of deep-sea hydrothermal vents 200 miles offshore from Fuget Sound, comes a newly discovered liyperthermophilic—or extreme heat-loving—microbe that holds the record for the hottest existence known to science. This microbe is tentatively known as Strain 121 for the temperature at which it thrives: 121 °C. (At sea level, water at this temperature would boil vigorously, but the extreme pressures at the ocean floor prevent boiling from occurring.) What is this temperature in degrees Fahrenheit?
Solution:
Chapter 16 Temperature and Heat Q.72GP
The heat Q will warm 1 g of material A by 1 C°, the heat 2Q will warm 3 g of material B by 3 C°, the heat 3Q will warm 3 g of material C by 1 C°, arid the heat 4Q will warm 4 g of material D by 2 C°. Rank these materials in order of increasing specific heat. Indicate ties where appropriate.
Solution:
Chapter 16 Temperature and Heat Q.73GP
many biological systems it is of more interest to know how much heat is required to raise the temperature of a given volume of material rather than a given mass of material. Calculate the heat needed to raise the temperature of one cubic meter of (a) air and (b) water by one degree Ceisius. Compare with the corresponding specific heats {for a given mass) listed in Table 16-2.
Solution:
Chapter 16 Temperature and Heat Q.74GP
As you read this problem, your brain is consuming about 22 W of power, (a) How many steps with a height of 21 cm. must you climb to expend a mechanical energy equivalent to one hour of brain operation? (b) A typical human brain, which is 77% water, has a mass of 1.4 kg. Assuming that the 22 W of brain power is converted to heat, what temperature rise would you estimate for the brain in one hour of operation? Ignore the significant heat transfer that occurs between a human head and its surroundings, as weil as the 23% of the brain that is not water.
Solution:
Chapter 16 Temperature and Heat Q.75GP
Solution:
Chapter 16 Temperature and Heat Q.76GP
If heat is transferred to 150 g of water at a constant rate for 2.5 min, its temperature increases by 13 C°. When heat is transferred at the same rate for the same amount of time to a 150-g object of unknown material, its temperature increases by 61 C°. (a) From whatmaterial. is the object made? (b) What is the heating rate?
Solution:
Chapter 16 Temperature and Heat Q.77GP
Apendulum consists of a large weight suspended by a steel wire that is 0.9500 in long, (a) If the tempera ture increases, does the period of the pendulum increase, decrease, or stay the same? Explain, (b) Calculate the change in length of the pendulum if the temperature increase is 150.0 C°. (c) Calculate the period of the pendulum before and after the temperature increase. (Assume that the coefficient of linear expansion for the wire is 12.00 × 10−6 K−1, and that g = 9.810 m/s2 at the location of the pendulum.)
Solution:
Chapter 16 Temperature and Heat Q.78GP
Once the aluminum ring in Problem 19 is slipped over the bar, the ring and bar are allowed to equilibrate at a temperature of 22 °C- The ring is now stuck on the bar. (a) If the temperatures of both the ring and the bar are changed together, should the system be heated or cooled to remove the ring? (b) Find the temperature at which the ring can be removed.
Solution:
Chapter 16 Temperature and Heat Q.79GP
A steel plate has a circular hole with a diameter of 1.000 cm In order to drop a Pyrex glass marble 1.003 cm in diameter. through the hole in the plate, how much must the temperature of the system be raised? (Assume the plate and the marble are always at the same tempera ture.)
Solution:
Chapter 16 Temperature and Heat Q.80GP
A226-kg rock sits in Ml sunlight on the edge of a cliff 5.25 m high. The temperature of the rock is 30.2 °C If the rock falls from the cliff into a pool containing 6.00 m3 of water at 15.5 °C, what is the final temperature of the rock-water system? Assume that the specific heat of the rock is 1010 J/(kg · K).
Solution:
Chapter 16 Temperature and Heat Q.81GP
Water going over Iguacu Falls on the border of Argentina and Brazil drops through a height of about 72 m. Suppose that all the gravitational potential energy of the water goes into raising its temperature. Find the increase in water temperature at the bottom of the falls as compared with the top.
Solution:
Chapter 16 Temperature and Heat Q.82GP
A 0.22-kg steel pot on a stove contains 2.1 L of water at 22 °C. When the burner is turned on, the water begins to boil after 8.5 minutes, (a) At what rate is heatbeing transferred from the burner to the pot of water? (b) At this rate of heating, would it take more time or less time for the water to start to boil if the pot were made of gold rather than steel?
Solution:
Chapter 16 Temperature and Heat Q.83GP
Suppose you could convert the 525 Calories in the cheeseburger you ate for lunch into mechanical energy with 100% efficiency, (a) How high could you throw a 0.145-kg baseball with the energy contained in the cheeseburger? (b) How fast would the ball be moving at the moment of release?
Solution:
Chapter 16 Temperature and Heat Q.84GP
You turn a crank on a device similar to that shown in Figure 16-8 and produce a power of 0.18 hp. If the paddles are immersed in 0.65 kg of water, for what length of time must you turn the crank to increase the temperature of the water by 5.0 C°?
Solution:
Chapter 16 Temperature and Heat Q.85GP
The core temperature of the human body is 37.0 °C, and the skin, with a surface area of 1.40 m2, has a temperature of 34.0 °C. (a) Find the rate of heat transfer out of the body under the following assumptions: (i) The average thickness of tissue between the core and the skin is 1.20 cm; (ii) the thermal conductivity of the tissue is that of water. (b) Without repea ting the calculation of part (a), what rate of heat transfer would you expect if the skin temperature were to fall to 31.0 °C? Explain.
Solution:
Chapter 16 Temperature and Heat Q.86GP
The surface of the Sun has a temperature of 5500 °C. (a) Treating the Sun as a perfect blackbody, with an emissivity of 1.0, find the power that it radiates into space. The radius of the Sun is 7.0 × 108 m, and the temperature of space can be taken to be 3.0 K. (b) The solar constant is the number of watts of sunlight power falling on a square meter of the Earth’s upper atmosphere. Use your result from part (a) to calculate the solar constant, given that the distance from the Sun to the Earth is 1.5 × 1011 m.
Solution:
Chapter 16 Temperature and Heat Q.87GP
Solution:
Chapter 16 Temperature and Heat Q.88GP
A grandfather clock has a simple brass pendulum of length L. One night, the temperature in the house is 25.0 °C and the period of the pendulum is 1.00 s. The dock keeps correct time at this temperature. If the temperature in the house quickly drops to 17.1 °C just after 10 P.M., and stays at that value, what is the actual time when the clock indicates that it is 10 A.M. the next morning?
Solution:
Chapter 16 Temperature and Heat Q.89GP
Solution:
Chapter 16 Temperature and Heat Q.90GP
A layer of ice has formed on a small pond. The air just above the ice is at -5.4 °C, the water-ice interface is at 0 °C, and the water at the bottom of the pond is at 4.0 °C. If the total depth from the top of the ice to the bottom of the pond is 1.4 m, how thick is the layer of ice? Note; The thermal conductivity of ice is 1.6 W/(m · C°) and that of water is 0.60 W/(m · C°).
Solution:
Chapter 16 Temperature and Heat Q.91GP
Solution:
Chapter 16 Temperature and Heat Q.92PP
How hot is the Blackbird when it lands, assuming it is 8.0 inches longer than at takeoff, its coefficient of linear expansion is 22 × 10−6 K−1, and its temperature at takeoff is 23 °C?
A. 280 °C
B. 310 °C
C. 560 °C
D. 3400 °C
Solution:
Chapter 16 Temperature and Heat Q.93PP
If the SR-71 were painted white instead of black, would its in-flight temperature be greater than, less than, or equal to its temperature with black paint?
Solution:
Picture the problem:
According to the problem, the blackbird SR-71 was painted white instead of black. We can observe the difference in the temperature when the blackbird is filled with the above two colours and it can be known by using the concept of radiation.
Strategy:
A Black body is a perfect emitter and a perfect absorber. This property of the blackbody is valid for radiation corresponding to all wavelengths and to all the incident angles.
Solution:
A perfect white body neither emits nor absorbs any radiation, whereas a blackbody is a perfect emitter and a perfect absorber. So, the blackbody emits the radiation incident on it which is not the case for a white body. Because, the white body is not a perfect emitter, the in flight temperature remains the same as the temperature at the time of its take off and it will be greater than that of the in flight temperature of the blackbird painted in black.
Chapter 16 Temperature and Heat Q.94PP
Choose the best explanation for the previous problem from among the following:
A. Heating by airresistance is the same for any color of paint; therefore, the plane will have the same temperature regardless of color.
B. Black is a more efficient radiator of heat than white. Therefore, the black paint radiates more heat, and allows the airplane to stay cooler.
C. Black objects are generally hotter than white ones, all other tilings being equal. Therefore, the plane would be cooler with white paint.
Solution:
Picture the problem:
We can observe the difference in the temperatures of the blackbird when it is coloured with white and black. This can be known in detail by using the concept of radiation.
Strategy:
A Black body is a perfect emitter and a perfect absorber. This property of the blackbody is valid for radiation corresponding to all wavelengths and to all the incident angles.
Solution:
A perfect white body neither emits nor absorbs any radiation, whereas a blackbody is a perfect emitter and a perfect absorber. So, the blackbody emits the radiation incident on it which is not the case for a white body. Because, the white body is not a perfect emitter, the in flight temperature remains the same as the temperature at the time of its take off and it will be greater than that of the in flight temperature of the blackbird painted in black.
Therefore, the black paint radiates more heat, and allows the plane to stay cooler.
The correct option is (B)
Chapter 16 Temperature and Heat Q.95PP
How long is the Blackbird when it is 120 °C?
A. 107 ft 7.8 in.
B. 107 ft 8.2 in.
C. 108 ft 0.8 in.
D. 108 ft 1.4 in.
Solution:
Chapter 16 Temperature and Heat Q.96IP
Suppose the mass of the block is to be increased enough to make the final temperature of the system equal to 22.5 °C. What is the required mass? Everything else in Example remains the same.
Solution:
Chapter 16 Temperature and Heat Q.97IP
Suppose the initial temperature of the block is to be increased enough to make the final temperature of the system equal to 22.5 °C. What is the required initial temperature? Everything else remains the same as in Example.
Solution:
Chapter 16 Temperature and Heat Q.98IP
Suppose the lead rod is replaced with a second copper rod. (a) Will the heat that flows in 1.00 s increase, decrease, or stay the same? Explain, (b) Find the heat that flows in 1.00 s with two copper rods. Everything else remains the same as in Example.
Solution:
Chapter 16 Temperature and Heat Q.99IP
Suppose the temperature of the hot plate is to be changed to give a total heat flow of 25.2 J in 1.00 s. (a) Should the new temperature of the hot plate be greater than or less than 106 °C? Explain, (b) Find the required temperature of the hot plate. Everything else is the same as in Example.
Solution:
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