Solved: A person eats a container of strawberry yogurt.

A healthy person has an oral temperature of 98.6 F. What would this reading be on the Celsius scale?

A time and temperature sign on a bank indicates that the outdoor temperature is 20.0 C. Find the corresponding temperature on the Fahrenheit scale.

Determine the magnitude of the difference between the stated temperature and the ice point on the initial scale.

Convert this number of degrees from one scale to the other scale by using the appropriate conversion factor. For conversion between the Celsius and Fahrenheit scales, the factor is based on the fact that 1 C 9 5 F. C

Add or subtract the number of degrees on the new scale to or from the ice point on the new scale.

On a new temperature scale the steam point is 348 X, and the ice point is 112 X. What is the temperature on this scale that corresponds to 28.0 C? Th

A concrete sidewalk is constructed between two buildings on a day when the temperature is 25 C. The sidewalk consists of two slabs, each three meters in length and of negligible thickness (Figure 12.11a). As the temperature rises to 38 C, the slabs expand, but no space is provided for thermal expansion. The buildings do not move, so the slabs buckle upward. Determine the vertical distance y in part b of the drawing. E

A steel beam is used in the roadbed of a bridge. The beam is mounted between two concrete supports when the temperature is 23 C, with no room provided for thermal expansion (see Figure 12.14). What compressional stress must the concrete supports apply to each end of the beam, if they are to keep the beam from expanding when the temperature rises to 42 C? Assume that the distance between the concrete supports does not change as the temperature rises.

Figure 12.17a shows eight square tiles that are attached together and arranged to form a square pattern with a hole in the center. If the tiles are heated, does the size of the hole (a) decrease or (b) increase?

A gold engagement ring has an inner diameter of 1.5  102 m and a temperature of 27 C. The ring falls into a sink of hot water whose temperature is 49 C. What is the change in the diameter of the hole in the ring?

Figure 12.18 shows a cross-sectional view of three cylinders, A, B, and C. One is made from lead, one from brass, and one from steel. All three have the same temperature, and they barely fit inside each other. As the cylinders are heated to the same higher temperature, C falls off, while A becomes tightly wedged against B. Which cylinder is made from which material? (a) A is brass, B is lead, C is steel (b) A is lead, B is brass, C is steel (c) A is lead, B is steel, C is brass (d) A is brass, B is steel, C is lead (e) A is steel, B is brass, C is lead (f) A is steel, B is lead, C is brass

A rod is hung from an aluminum frame, as the drawing shows. The rod and the frame have the same temperature, and there is a small gap between the rod and the floor. The frame and rod are then heated uniformly. Will the rod ever touch the floor if the rod is made from (a) aluminum, (b) lead, (c) brass?

A simple pendulum is made using a long, thin metal wire. When the temperature drops, does the period of the pendulum increase, decrease, or remain the same?

For added strength, many highways and buildings are constructed with reinforced concrete (concrete that is reinforced with embedded steel rods). Table 12.1 shows that the coefficient of linear expansion for concrete is the same as that for steel. Why is it important that these two coefficients be the same?

One type of cooking pot is made from stainless steel and has a copper coating over the outside of the bottom. At room temperature the bottom of this pot is flat, but when heated the bottom is not flat. When the bottom of this pot is heated, is it bowed outward or inward?

A metal ball has a diameter that is slightly greater than the diameter of a hole that has been cut into a metal plate. The coefficient of linear expansion for the metal from which the ball is made is greater than that for the metal of the plate. Which one or more of the following procedures can be used to make the ball pass through the hole? (a) Raise the temperatures of the ball and the plate by the same amount. (b) Lower the temperatures of the ball and the plate by the same amount. (c) Heat the ball and cool the plate. (d) Cool the ball and heat the plate.

A hole is cut through an aluminum plate. A brass ball has a diameter that is slightly smaller than the diameter of the hole. The plate and the ball have the same temperature at all times. Should the plate and ball both be heated or both be cooled to prevent the ball from falling through the hole?

A small plastic container, called the coolant reservoir, catches the radiator fluid that overflows when an automobile engine becomes hot (see Figure 12.19). The radiator is made of copper, and the coolant has a coefficient of volume expansion of 4.10  104 (C) 1 . If the radiator is filled to its 15-quart capacity when the engine is cold (6.0 C), how much overflow will spill into the reservoir when the coolant reaches its operating temperature of 92 C? Exam

In a half hour, a 65-kg jogger can generate 8.0  105 J of heat. This heat is removed from the joggers body by a variety of means, including the bodys own temperature-regulating mechanisms. If the heat were not removed, how much would the joggers body temperature increase?

Cold water at a temperature of 15 C enters a heater, and the resulting hot water has a temperature of 61 C. A person uses 120 kg of hot water in taking a shower. (a) Find the energy needed to heat the water. (b) Assuming that the utility company charges $0.10 per kilowatt hour for electrical energy, determine the cost of heating the water.

Figure 12.24 shows a swimming pool on a sunny day. If the water absorbs 2.00  109 J of heat from the sun, what is the change in the volume of the water?

The calorimeter cup in Figure 12.25 is made from 0.15 kg of aluminum and contains 0.20 kg of water. Initially, the water and the cup have a common temperature of 18.0 C. A 0.040-kg mass of unknown material is heated to a temperature of 97.0 C and then added to the water. The temperature of the water, the cup, and the unknown material is 22.0 C after thermal equilibrium is reestablished. Ignoring the small amount of heat gained by the thermometer, find the specific heat capacity of the unknown material.

Two different objects are supplied with equal amounts of heat. Which one or more of the following statements explain why their temperature changes would not necessarily be the same? (a) The objects have the same mass but are made from materials that have different specific heat capacities. (b) The objects are made from the same material but have different masses. (c) The objects have the same mass and are made from the same material.

Two objects are made from the same material but have different masses. The two are placed in contact, and neither one loses any heat to the environment. Which object experiences the temperature change with the greater magnitude, or does each object experience a temperature change of the same magnitude?

Consider an object of mass m that experiences a change T in its temperature. Various possibilities for these variables are listed in the table. Rank these possibilities in descending order (largest first) according to how much heat is needed to bring about the change in temperature.

Suppose you are cooking spaghetti, and the instructions say boil the pasta in water for ten minutes. To cook spaghetti in an open pot using the least amount of energy, should you (a) turn up the burner to its fullest so the water vigorously boils or (b) turn down the burner so the water barely boils?

Ice at 0 C is placed in a Styrofoam cup containing 0.32 kg of lemonade at 27 C. The specific heat capacity of lemonade is virtually the same as that of water; that is, c 4186 J/(kg C). After the ice and lemonade reach an equilibrium temperature, some ice still remains. The latent heat of fusion for water is Lf 3.35 105 J/kg. Assume that the mass of the cup is so small that it absorbs a negligible amount of heat, and ignore any heat lost to the surroundings. Determine the mass of ice that has melted.

A 7.00-kg glass bowl [c 840 J/(kg C)] contains 16.0 kg of punch at 25.0 C. Two-and-a-half kilograms of ice [c 2.00 103 J/(kg C)] are added to the punch. The ice has an initial temperature of 20.0 C, having been kept in a very cold freezer. The punch may be treated as if it were water [c 4186 J/(kg C)], and it may be assumed that there is no heat flow between the punch bowl and the external environment. The latent heat of fusion for water is 3.35 105 J/kg. When thermal equilibrium is reached, all the ice has melted, and the final temperature of the mixture is above 0 C. Determine this temperature. Exa

Fruit blossoms are permanently damaged at temperatures of about 4 C (a hard freeze). Orchard owners sometimes spray a film of water over the blossoms to protect them when a hard freeze is expected. Why does this technique offer protection?

When ice cubes are used to cool a drink, both their mass and temperature are important in how effective they are. The table lists several possibilities for the mass and temperature of the ice cubes used to cool one particular drink. Rank the possibilities in descending order (best first) according to their cooling effectiveness. Note that the latent heat of phase change and the specific heat capacity must be considered.

Figure 12.33a shows water boiling in an open flask. Shortly after the flask is removed from the burner, the boiling stops. A cork is then placed in the neck of the flask to seal it, and water is poured over the neck of the flask, as in part b of the drawing. To restart the boiling, should the water poured over the neck be (a) cold or (b) hotbut not boiling?

A camping stove is used to boil water high on a mountain, where the atmospheric pressure is lower than it is at sea level. Does it necessarily follow that the same stove can boil water at sea level?

Medical instruments are sterilized at a high temperature in an autoclave, which is essentially a pressure cooker that heats the instruments in water under a pressure greater than one atmosphere. Why is the water in an autoclave able to reach a very high temperature, while water in an open pot can only be heated to 100 C? 1

A jar is half filled with boiling water. The lid is then screwed on the jar. After the jar has cooled to room temperature, the lid is difficult to remove. Why? Ignore the thermal expansion and contraction of the jar and the lid.

A bottle of carbonated soda (sealed and under a pressure greater than one atmosphere) is left outside in subfreezing temperatures, although the soda remains liquid. When the soda is brought inside and opened immediately, it suddenly freezes. Why?

When a bowl of water is placed in a closed container and the water vapor is pumped away rapidly enough, why does the remaining liquid turn into ice?

One day, the partial pressure of water vapor in the air is 2.0  103 Pa. Using the vaporization curve for water in Figure 12.36, determine the relative humidity if the temperature is (a) 32 C and (b) 21 C.

A bowl of water is covered tightly and allowed to sit at a constant temperature of 23 C for a long time. What is the relative humidity in the space between the surface of the water and the cover?

Is it possible for dew to form on Tuesday night and not on Monday night, even though Monday night is the cooler night?

Two rooms in a mansion have the same temperature. One of these rooms contains an indoor swimming pool. On a cold day the windows of one of the two rooms are steamed up. Which room is it likely to be? Explain.

Figure 12.39 shows three rectangular blocks made from the same material. The initial dimensions of each are expressed as multiples of D, where D 2.00 cm. The blocks are heated and their temperatures increase by 35.0 C. The coefficients of linear and volume expansion are and respectively. Determine the change in the (a) vertical heights and (b) volumes of the blocks.

Does the change in the vertical height of a block depend only on its height, or does it also depend on its width and depth? Without doing any calculations, rank the blocks according to their change in height, largest first.

Does the change in the volume of a block depend only on its height, or does it also depend on its width and depth? Without doing any calculations, rank the blocks according to their greatest change in volume, largest first.

Objects A and B in Figure 12.40 are made from copper, but the mass of object B is three times the mass of object A. Object C is made from glass and has the same mass as object B. The same amount of heat Q is supplied to each one: Q 14 J. Determine the rise in temperature for each.

Which object, A or B, experiences the greater rise in temperature

Which object, B or C, experiences the greater rise in temperature?

Which one of the following statements correctly describes the Celsius and the Kelvin temperature scales? (a) The size of the degree on the Celsius scale is larger than that on the Kelvin scale by a factor of 9/5. (b) Both scales assign the same temperature to the ice point, but they assign different temperatures to the steam point. (c) Both scales assign the same temperature to the steam point, but they assign different temperatures to the ice point. (d) The Celsius scale assigns the same values to the ice and the steam points that the Kelvin scale assigns. (e) The size of the degree on each scale is the same.

The drawing shows two thin rods, one made from aluminum [ 23 106 (C) 1 ] and the other from steel [ 12 106 (C) 1 ]. Each rod has the same length and the same initial temperature and is attached at one end to an immovable wall, as shown. The temperatures of the rods are increased, both by the same amount, until the gap between the rods is closed. Where do the rods meet when the gap is closed? (a) The rods meet exactly at the midpoint. (b) The rods meet to the right of the midpoint. (c) The rods meet to the left of the midpoint. 4. A

A ball is slightly too large to fit through a hole in a flat plate. The drawing shows two arrangements of this situation. In Arrangement I the ball is made from metal A and the plate from metal B. When both the ball and the plate are cooled by the same number of Celsius degrees, the ball passes through the hole. In Arrangement II the ball is also made from metal A, but the plate is made from metal C. Here, the ball passes through the hole when both the ball and the plate are heated by the same number of Celsius degrees. Rank the coefficients of linear thermal expansion of metals A, B, and C in descending order (largest first): (a) B, A, C (b) B, C, A (c) C, B, A (d) C, A, B (e) A, B, C Section 12.5 V

A solid sphere and a solid cube are made from the same material. The sphere would just fit within the cube, if it could. Both begin at the same temperature, and both are heated to the same temperature. Which object, if either, has the greater change in volume? (a) The sphere. (b) The cube. (c) Both have the same change in volume. (d) Insufficient information is given for an answer.

A container can be made from steel [ 36 106 (C) 1 ] or lead [ 87 106 (C) 1 ]. A liquid is poured into the container, filling it to the brim. The liquid is either water [ 207 106 (C) 1 ] or ethyl alcohol [ 1120 106 (C) 1 ]. When the full container is heated, some liquid spills out. To keep the overflow to a minimum, from what material should the container be made and what should the liquid be? (a) Lead, water (b) Steel, water (c) Lead, ethyl alcohol (d) Steel, ethyl alcohol Focus on Co

Which of the following cases (if any) requires the greatest amount of heat? In each case the material is the same. (a) 1.5 kg of the material is to be heated by 7.0 C. (b) 3.0 kg of the material is to be heated by 3.5 C. (c) 0.50 kg of the material is to be heated by 21 C. (d) 0.75 kg of the material is to be heated by 14 C. (e) The amount of heat required is the same in each of the four previous cases.

The following three hot samples have the same temperature. The same amount of heat is removed from each sample. Which one experiences the smallest drop in temperature, and which one experiences the largest drop? Sample A. 4.0 kg of water [c 4186 J/(kg C)] Sample B. 2.0 kg of oil [c 2700 J/(kg C)] Sample C. 9.0 kg of dirt [c 1050 J/(kg C)] (a) C smallest and A largest (b) B smallest and C largest (c) A smallest and B largest (d) C smallest and B largest (e) B smallest and A largest Se

The latent heat of fusion for water is 33.5 104 J/kg, while the latent heat of vaporization is 22.6 105 J/kg. What mass m of water must be frozen in order to release the amount of heat that 1.00 kg of steam releases when it condenses? S

Which one or more of the following techniques can be used to freeze water? A. Cooling the water below its normal freezing point of 0 C at the normal atmospheric pressure of 1.01 105 Pa B. Cooling the water below its freezing point of 1 C at a pressure greater than 1.01 105 Pa C. Rapidly pumping away the water vapor above the liquid in an insulated container (The insulation prevents heat flowing from the surroundings into the remaining liquid.) (a) Only A (b) Only B (c) Only A and B (d) A, B, and C (e) Only C S

Which of the following three statements concerning relative humidity values of 30% and 40% are true? Note that when the relative humidity is 30%, the air temperature may be different than it is when the relative humidity is 40%. A. It is possible that at a relative humidity of 30% there is a smaller partial pressure of water vapor in the air than there is at a relative humidity of 40%. B. It is possible that there is the same partial pressure of water vapor in the air at 30% and at 40% relative humidity. C. It is possible that at a relative humidity of 30% there is a greater partial pressure of water vapor in the air than there is at a relative humidity of 40%. (a) A, B, and C (b) Only A and B (c) Only A and C (d) Only B and C (e) Only A

Suppose you are hiking down the Grand Canyon. At the top, the temperature early in the morning is a cool 3 C. By late afternoon, the temperature at the bottom of the canyon has warmed to a sweltering 34 C. What is the difference between the higher and lower temperatures in (a) Fahrenheit degrees and (b) kelvins?

You are sick, and your temperature is 312.0 kelvins. Convert this temperature to the Fahrenheit scale.

On the moon the surface temperature ranges from 375 K during the day to 1.00  102 K at night. What are these temperatures on the (a) Celsius and (b) Fahrenheit scales?

Whats your normal body temperature? It may not be 98.6 F, the often-quoted average that was determined in the nineteenth century. A more recent study has reported an average temperature of 98.2 F. What is the difference between these averages, expressed in Celsius degrees?

Dermatologists often remove small precancerous skin lesions by freezing them quickly with liquid nitrogen, which has a temperature of 77 K. What is this temperature on the (a) Celsius and (b) Fahrenheit scales?

The drawing shows two thermometers, A and B, whose temperatures are measured in A and B. The ice and boiling points of water are also indicated. (a) Using the data in the drawing, determine the number of B degrees on the B scale that correspond to 1 A on the A scale. (b) If the temperature of a substance reads 40.0 A on the A scale, what would that temperature read on the B scale?

A copperconstantan thermocouple generates a voltage of 4.75  10 3 volts when the temperature of the hot junction is 110.0 C and the reference junction is kept at a temperature of 0.0 C. If the voltage is proportional to the difference in temperature between the junctions, what is the temperature of the hot junction when the voltage is 1.90  10 3 volts?

If a nonhuman civilization were to develop on Saturns largest moon, Titan, its scientists might well devise a temperature scale based on the properties of methane, which is much more abundant on the surface than water is. Methane freezes at 182.6 C on Titan, and boils at 155.2 C. Taking the boiling point of methane as 100.0 M (degrees Methane) and its freezing point as 0 M, what temperature on the Methane scale corresponds to the absolute zero point of the Kelvin scale?

On the Rankine temperature scale, which is sometimes used in engineering applications, the ice point is at 491.67 R and the steam point is at 671.67 R. Determine a relationship (analogous to Equation 12.1) between the Rankine and Fahrenheit temperature scales.

A steel section of the Alaskan pipeline had a length of 65 m and a temperature of 18 C when it was installed. What is its change in length when the temperature drops to a frigid 45 C?

A steel aircraft carrier is 370 m long when moving through the icy North Atlantic at a temperature of 2.0 C. By how much does the carrier lengthen when it is traveling in the warm Mediterranean Sea at a temperature of 21 C?

The Eiffel Tower is a steel structure whose height increases by 19.4 cm when the temperature changes from 9 to 41 C. What is the approximate height (in meters) at the lower temperature?

Conceptual Example 5 provides background for this problem. A hole is drilled through a copper plate whose temperature is 11 C. (a) When the temperature of the plate is increased, will the radius of the hole be larger or smaller than the radius at 11 C? Why? (b) When the plate is heated to 110 C, by what fraction r/r0 will the radius of the hole change?

A commonly used method of fastening one part to another part is called shrink fitting. A steel rod has a diameter of 2.0026 cm, and a flat plate contains a hole whose diameter is 2.0000 cm. The rod is cooled so that it just fits into the hole. When the rod warms up, the enormous thermal stress exerted by the plate holds the rod securely to the plate. By how many Celsius degrees should the rod be cooled?

When the temperature of a coin is raised by 75 C, the coins diameter increases by 2.3  10 5 m. If the original diameter of the coin is 1.8  10 2 m, find the coefficient of linear expansion.

One January morning in 1943, a warm chinook wind rapidly raised the temperature in Spearfish, South Dakota, from below freezing to 12.0 C. As the chinook died away, the temperature fell to 20.0 C in 27.0 minutes. Suppose that a 19-m aluminum flagpole were subjected to this temperature change. Find the average speed at which its height would decrease, assuming the flagpole responded instantaneously to the changing temperature.

One rod is made from lead and another from quartz. The rods are heated and experience the same change in temperature. The change in length of each rod is the same. If the initial length of the lead rod is 0.10 m, what is the initial length of the quartz rod?

A thin rod consists of two parts joined together. One-third of it is silver and two-thirds is gold. The temperature decreases by 26 C. Determine the fractional decrease in the rods length, where L0, Silver and L0, Gold are the initial lengths of the silver and gold rods.

The brass bar and the aluminum bar in the drawing are each attached to an immovable wall. At 28 C the air gap between the rods is 1.3  10 3 m. At what temperature will the gap be closed?

Multiple-Concept Example 4 reviews the concepts that are involved in this problem. A ruler is accurate when the temperature is 25 C. When the temperature drops to 14 C, the ruler shrinks and no longer measures distances accurately. However, the ruler can be made to read correctly if a force of magnitude 1.2  103 N is applied to each end so as to stretch it back to its original length. The ruler has a cross-sectional area of 1.6  10 5 m2 , and it is made from a material whose coefficient of linear expansion is 2.5  10 5 (C) 1 . What is Youngs modulus for the material from which the ruler is made?

A simple pendulum consists of a ball connected to one end of a thin brass wire. The period of the pendulum is 2.0000 s. The temperature rises by 140 C, and the length of the wire increases. Determine the period of the heated pendulum.

As the drawing shows, two thin strips of metal are bolted together at one end; both have the same temperature. One is steel, and the other is aluminum. The steel strip is 0.10% longer than the aluminum strip. By how much should the temperature of the strips be increased, so that the strips have the same length?

Consult Conceptual Example 5 for background pertinent to this problem. A lead sphere has a diameter that is 0.050% larger than the inner diameter of a steel ring when each has a temperature of 70.0 C. Thus, the ring will not slip over the sphere. At what common temperature will the ring just slip over the sphere?

Consult Multiple-Concept Example 4 for insight into solving this problem. A copper rod is fastened securely at both ends to immovable supports. When this rod is stretched, it will rupture when a tensile stress of 2.3  107 N/m2 is applied at each end. The rod just fits between the supports, so initially there is no stress applied to the rod. The rod is then cooled. What is the magnitude |T | of the change in temperature of the rod when it ruptures?

A ball and a thin plate are made from different materials and have the same initial temperature. The ball does not fit through a hole in the plate, because the diameter of the ball is slightly larger than the diameter of the hole. However, the ball will pass through the hole when the ball and the plate are both heated to a common higher temperature. In each of the arrangements in the drawing the diameter of the ball is 1.0  10 5 m larger than the diameter of the hole in the thin plate, which has a diameter of 0.10 m. The initial temperature of each arrangement is 25.0 C. At what temperature will the ball fall through the hole in each arrangement?

An 85.0-N backpack is hung from the middle of an aluminum wire, as the drawing shows. The temperature of the wire then drops by 20.0 C. Find the tension in the wire at the lower temperature. Assume that the distance between the supports does not change, and ignore any thermal stress.

A steel ruler is calibrated to read true at 20.0 C. A draftsman uses the ruler at 40.0 C to draw a line on a 40.0 C copper plate. As indicated on the warm ruler, the length of the line is 0.50 m. To what temperature should the plate be cooled, such that the length of the line truly becomes 0.50 m?

A flask is filled with 1.500 L (L liter) of a liquid at 97.1 C. When the liquid is cooled to 15.0 C, its volume is only 1.383 L, however. Neglect the contraction of the flask and use Table 12.1 to identify the liquid.

A thin spherical shell of silver has an inner radius of 2.0  10 2 m when the temperature is 18 C. The shell is heated to 147 C. Find the change in the interior volume of the shell.

A test tube contains 2.54  10 4 m3 of liquid carbon tetrachloride at a temperature of 75.0 C. The test tube and the carbon tetrachloride are cooled to a temperature of 13.0 C, which is above the freezing point of carbon tetrachloride. Find the volume of carbon tetrachloride in the test tube at 13.0 C.

A copper kettle contains water at 24 C. When the water is heated to its boiling point of 100.0 C, the volume of the kettle expands by 1.2  10 5 m3 . Determine the volume of the kettle at 24 C.

Suppose you are selling apple cider for two dollars a gallon when the temperature is 4.0 C. The coefficient of volume expansion of the cider is 280  10 6 (C) 1 . How much more money (in pennies) would you make per gallon by refilling the container on a day when the temperature is 26 C? Ignore the expansion of the container.

During an all-night cram session, a student heats up a onehalf liter (0.50  10 3 m3 ) glass (Pyrex) beaker of cold coffee. Initially, the temperature is 18 C, and the beaker is filled to the brim. A short time later when the student returns, the temperature has risen to 92 C. The coefficient of volume expansion of coffee is the same as that of water. How much coffee (in cubic meters) has spilled out of the beaker?

Many hot-water heating systems have a reservoir tank connected directly to the pipeline, to allow for expansion when the water becomes hot. The heating system of a house has 76 m of copper pipe whose inside radius is 9.5  10 3 m. When the water and pipe are heated from 24 to 78 C, what must be the minimum volume of the reservoir tank to hold the overflow of water?

Suppose that the steel gas tank in your car is completely filled when the temperature is 17 C. How many gallons will spill out of the twenty-gallon tank when the temperature rises to 35 C?

An aluminum can is filled to the brim with a liquid. The can and the liquid are heated so their temperatures change by the same amount. The cans initial volume at 5 C is 3.5  10 4 m3 . The coefficient of volume expansion for aluminum is 69  10 6 (C) 1 . When the can and the liquid are heated to 78 C, 3.6  10 6 m3 of liquid spills over. What is the coefficient of volume expansion of the liquid?

A spherical brass shell has an interior volume of 1.60  10 3 m3 . Within this interior volume is a solid steel ball that has a volume of 0.70  10 3 m3 . The space between the steel ball and the inner surface of the brass shell is filled completely with mercury. A small hole is drilled through the brass, and the temperature of the arrangement is increased by 12 C. What is the volume of the mercury that spills out of the hole?

At the bottom of an old mercury-in-glass thermometer is a 45-mm3 reservoir filled with mercury. When the thermometer was placed under your tongue, the warmed mercury would expand into a very narrow cylindrical channel, called a capillary, whose radius was 1.7  10 2 mm. Marks were placed along the capillary that indicated the temperature. Ignore the thermal expansion of the glass and determine how far (in mm) the mercury would expand into the capillary when the temperature changed by 1.0 C

The density of mercury is 13 600 kg/m3 at 0 C. What would its density be at 166 C?

Two identical thermometers made of Pyrex glass contain, respectively, identical volumes of mercury and methyl alcohol. If the expansion of the glass is taken into account, how many times greater is the distance between the degree marks on the methyl alcohol thermometer than the distance on the mercury thermometer?

The column of mercury in a barometer (see Figure 11.11) has a height of 0.760 m when the pressure is one atmosphere and the temperature is 0.0 C. Ignoring any change in the glass containing the mercury, what will be the height of the mercury column for the same one atmosphere of pressure when the temperature rises to 38.0 C on a hot day?

Ideally, when a thermometer is used to measure the temperature of an object, the temperature of the object itself should not change. However, if a significant amount of heat flows from the object to the thermometer, the temperature will change. A thermometer has a mass of 31.0 g, a specific heat capacity of c 815 J/(kg C), and a temperature of 12.0 C. It is immersed in 119 g of water, and the final temperature of the water and thermometer is 41.5 C. What was the temperature of the water before the insertion of the thermometer?

Blood can carry excess energy from the interior to the surface of the body, where the energy is dispersed in a number of ways. While a person is exercising, 0.6 kg of blood flows to the bodys surface and releases 2000 J of energy. The blood arriving at the surface has the temperature of the bodys interior, 37.0 C. Assuming that blood has the same specific heat capacity as water, determine the temperature of the blood that leaves the surface and returns to the interior.

An ice chest at a beach party contains 12 cans of soda at 5.0 C. Each can of soda has a mass of 0.35 kg and a specific heat capacity of 3800 J/(kg C). Someone adds a 6.5-kg watermelon at 27 C to the chest. The specific heat capacity of watermelon is nearly the same as that of water. Ignore the specific heat capacity of the chest and determine the final temperature T of the soda and watermelon.

A piece of glass has a temperature of 83.0 C. Liquid that has a temperature of 43.0 C is poured over the glass, completely covering it, and the temperature at equilibrium is 53.0 C. The mass of the glass and the liquid is the same. Ignoring the container that holds the glass and liquid and assuming that the heat lost to or gained from the surroundings is negligible, determine the specific heat capacity of the liquid.

When resting, a person has a metabolic rate of about 3.0  105 joules per hour. The person is submerged neck-deep into a tub containing 1.2  103 kg of water at 21.00 C. If the heat from the person goes only into the water, find the water temperature after half an hour.

Two bars of identical mass are at 25 C. One is made from glass and the other from another substance. The specific heat capacity of glass is 840 J/(kg C). When identical amounts of heat are supplied to each, the glass bar reaches a temperature of 88 C, while the other bar reaches 250.0 C. What is the specific heat capacity of the other substance?

At a fabrication plant, a hot metal forging has a mass of 75 kg and a specific heat capacity of 430 J/(kg C). To harden it, the forging is immersed in 710 kg of oil that has a temperature of 32 C and a specific heat capacity of 2700 J/(kg C). The final temperature of the oil and forging at thermal equilibrium is 47 C. Assuming that heat flows only between the forging and the oil, determine the initial temperature of the forging.

When you drink cold water, your body must expend metabolic energy in order to maintain normal body temperature (37 C) by warming up the water in your stomach. Could drinking ice water, then, substitute for exercise as a way to burn calories? Suppose you expend 430 kilocalories during a brisk hour-long walk. How many liters of ice water (0 C) would you have to drink in order to use up 430 kilocalories of metabolic energy? For comparison, the stomach can hold about 1 liter.

A 0.35-kg coffee mug is made from a material that has a specific heat capacity of 920 J/(kg C) and contains 0.25 kg of water. The cup and water are at 15 C. To make a cup of coffee, a small electric heater is immersed in the water and brings it to a boil in three minutes. Assume that the cup and water always have the same temperature and determine the minimum power rating of this heater.

Three portions of the same liquid are mixed in a container that prevents the exchange of heat with the environment. Portion A has a mass m and a temperature of 94.0 C, portion B also has a mass m but a temperature of 78.0 C, and portion C has a mass mC and a temperature of 34.0 C. What must be the mass of portion C so that the final temperature Tf of the three-portion mixture is Tf 50.0 C? Express your answer in terms of m; for example, mC 2.20 m. *

One ounce of a well-known breakfast cereal contains 110 Calories (1 food Calorie 4186 J). If 2.0% of this energy could be converted by a weight lifters body into work done in lifting a barbell, what is the heaviest barbell that could be lifted a distance of 2.1 m?

The heating element of a water heater in an apartment building has a maximum power output of 28 kW. Four residents of the building take showers at the same time, and each receives heated water at a volume flow rate of 14  10 5 m3 /s. If the water going into the heater has a temperature of 11 C, what is the maximum possible temperature of the hot water that each showering resident receives?

A rock of mass 0.20 kg falls from rest from a height of 15 m into a pail containing 0.35 kg of water. The rock and water have the same initial temperature. The specific heat capacity of the rock is 1840 J/(kg C). Ignore the heat absorbed by the pail itself, and determine the rise in the temperature of the rock and water.

A steel rod ( 7860 kg/m3 ) has a length of 2.0 m. It is bolted at both ends between immobile supports. Initially there is no tension in the rod, because the rod just fits between the supports. Find the tension that develops when the rod loses 3300 J of heat.

How much heat must be added to 0.45 kg of aluminum to change it from a solid at 130 C to a liquid at 660 C (its melting point)? The latent heat of fusion for aluminum is 4.0  105 J/kg.

Suppose that the amount of heat removed when 3.0 kg of water freezes at 0.0 C were removed from ethyl alcohol at its freezing/ melting point of 114.4 C. How many kilograms of ethyl alcohol would freeze?

To help prevent frost damage, fruit growers sometimes protect their crop by spraying it with water when overnight temperatures are expected to go below freezing. When the water turns to ice during the night, heat is released into the plants, thereby giving a measure of protection against the cold. Suppose a grower sprays 7.2 kg of water at 0 C onto a fruit tree. (a) How much heat is released by the water when it freezes? (b) How much would the temperature of a 180-kg tree rise if it absorbed the heat released in part (a)? Assume that the specific heat capacity of the tree is 2.5  103 J/(kg C) and that no phase change occurs within the tree itself.

a) Objects A and B have the same mass of 3.0 kg. They melt when 3.0  104 J of heat is added to object A and when 9.0  104 J is added to object B. Determine the latent heat of fusion for the substance from which each object is made. (b) Find the heat required to melt object A when its mass is 6.0 kg.

Find the mass of water that vaporizes when 2.10 kg of mercury at 205 C is added to 0.110 kg of water at 80.0 C.

A mass m 0.054 kg of benzene vapor at its boiling point of 80.1 C is to be condensed by mixing the vapor with water at 41 C. What is the minimum mass of water required to condense all of the benzene vapor? Assume that the mixing and condensation take place in a perfectly insulating container.

The latent heat of vaporization of H2O at body temperature (37.0 C) is 2.42  106 J/kg. To cool the body of a 75-kg jogger [average specific heat capacity 3500 J/(kg C)] by 1.5 C, how many kilograms of water in the form of sweat have to be evaporated?

A certain quantity of steam has a temperature of 100.0 C. To convert this steam into ice at 0.0 C, energy in the form of heat must be removed from the steam. If this amount of energy were used to accelerate the ice from rest, what would be the linear speed of the ice? For comparison, bullet speeds of about 700 m/s are common.

A thermos contains 150 cm3 of coffee at 85 C. To cool the coffee, you drop two 11-g ice cubes into the thermos. The ice cubes are initially at 0 C and melt completely. What is the final temperature of the coffee? Treat the coffee as if it were water.

A snow maker at a resort pumps 130 kg of lake water per minute and sprays it into the air above a ski run. The water droplets freeze in the air and fall to the ground, forming a layer of snow. If all the water pumped into the air turns to snow, and the snow cools to the ambient air temperature of 7.0 C, how much heat does the snow-making process release each minute? Assume that the temperature of the lake water is 12.0 C, and use 2.00  103 J/(kg C) for the specific heat capacity of snow.

A 42-kg block of ice at 0 C is sliding on a horizontal surface. The initial speed of the ice is 7.3 m/s and the final speed is 3.5 m/s. Assume that the part of the block that melts has a very small mass and that all the heat generated by kinetic friction goes into the block of ice. Determine the mass of ice that melts into water at 0 C.

Water at 23.0 C is sprayed onto 0.180 kg of molten gold at 1063 C (its melting point). The water boils away, forming steam at 100.0 C and leaving solid gold at 1063 C. What is the minimum mass of water that must be used?

An unknown material has a normal melting/freezing point of 25.0 C, and the liquid phase has a specific heat capacity of 160 J/(kg C). One-tenth of a kilogram of the solid at 25.0 C is put into a 0.150-kg aluminum calorimeter cup that contains 0.100 kg of glycerin. The temperature of the cup and the glycerin is initially 27.0 C. All the unknown material melts, and the final temperature at equilibrium is 20.0 C. The calorimeter neither loses energy to nor gains energy from the external environment. What is the latent heat of fusion of the unknown material?

When it rains, water vapor in the air condenses into liquid water, and energy is released. (a) How much energy is released when 0.0254 m (one inch) of rain falls over an area of 2.59  106 m2 (one square mile)? (b) If the average energy needed to heat one home for a year is 1.50  1011 J, how many homes could be heated for a year with the energy determined in part (a)?

It is claimed that if a lead bullet goes fast enough, it can melt completely when it comes to a halt suddenly, and all its kinetic energy is converted into heat via friction. Find the minimum speed of a lead bullet (initial temperature 30.0 C) for such an event to happen.

Equal masses of two different liquids have the same temperature of 25.0 C. Liquid A has a freezing point of 68.0 C and a specific heat capacity of 1850 J/(kg C). Liquid B has a freezing point of 96.0 C and a specific heat capacity of 2670 J/(kg C). The same amount of heat must be removed from each liquid in order to freeze it into a solid at its respective freezing point. Determine the difference Lf, A  Lf, B between the latent heats of fusion for these liquids.

Occasionally, huge icebergs are found floating on the oceans currents. Suppose one such iceberg is 120 km long, 35 km wide, and 230 m thick. (a) How much heat would be required to melt this iceberg (assumed to be at 0 C) into liquid water at 0 C? The density of ice is 917 kg/m3 . (b) The annual energy consumption by the United States is about 1.1  1020 J. If this energy were delivered to the iceberg every year, how many years would it take before the ice melted?

What atmospheric pressure would be required for carbon dioxide to boil at a temperature of 20 C? See the vapor pressure curve for carbon dioxide in the drawing.

At a temperature of 10 C the percent relative humidity is R10, and at 40 C it is R40. At each of these temperatures the partial pressure of water vapor in the air is the same. Using the vapor pressure curve for water that accompanies this problem, determine the ratio R10/R40 of the two humidity values.

What is the relative humidity on a day when the temperature is 30 C and the dew point is 10 C? Use the vapor pressure curve that accompanies Problem 75.

Suppose that air in the human lungs has a temperature of 37 C, and the partial pressure of water vapor has a value of 5.5103 Pa. What is the relative humidity in the lungs? Consult the vapor pressure curve for water that accompanies Problem 75.

The vapor pressure of water at 10 C is 1300 Pa. (a) What percentage of atmospheric pressure is this? Take atmospheric pressure to be 1.013 105 Pa. (b) What percentage of the total air pressure at 10 C is due to water vapor when the relative humidity is 100%? (c) The vapor pressure of water at 35 C is 5500 Pa. What is the relative humidity at this temperature if the partial pressure of water in the air has not changed from what it was at 10 C when the relative humidity was 100%?

The temperature of 2.0 kg of water is 100.0 C, but the water is not boiling, because the external pressure acting on the water surface is 3.0 105 Pa. Using the vapor pressure curve for water given in Figure 12.32, determine the amount of heat that must be added to the water to bring it to the point where it just begins to boil.

The temperature of the air in a room is 36 C. A person turns on a dehumidifier and notices that when the cooling coils reach 30 C, water begins to condense on them. What is the relative humidity in the room? Use the vapor pressure curve that accompanies Problem 75.

A woman has been outdoors where the temperature is 10 C. She walks into a 25 C house, and her glasses steam up. Using the vapor pressure curve for water that accompanies Problem 75, find the smallest possible value for the relative humidity of the room.

A container is fitted with a movable piston of negligible mass and radius r 0.061 m. Inside the container is liquid water in equilibrium with its vapor, as the drawing shows. The piston remains stationary with a 120-kg block on top of it. The air pressure acting on the top of the piston is one atmosphere. By using the vaporization curve for water in Figure 12.32, find the temperature of the water.

At a picnic, a glass contains 0.300 kg of tea at 30.0 C, which is the air temperature. To make iced tea, someone adds 0.0670 kg of ice at 0.0 C and stirs the mixture. When all the ice melts and the final temperature is reached, the glass begins to fog up, because water vapor condenses on the outer glass surface. Using the vapor pressure curve for water that accompanies Problem 75, ignoring the specific heat capacity of the glass, and treating the tea as if it were water, estimate the relative humidity.

A tall column of water is open to the atmosphere. At a depth of 10.3 m below the surface, the water is boiling. What is the temperature at this depth? Use the vaporization curve for water in Figure 12.32, as needed.

An aluminum baseball bat has a length of 0.86 m at a temperature of 17 C. When the temperature of the bat is raised, the bat lengthens by 0.000 16 m. Determine the final temperature of the bat.

A person eats a container of strawberry yogurt. The Nutritional Facts label states that it contains 240 Calories (1 Calorie 4186 J). What mass of perspiration would one have to lose to get rid of this energy? At body temperature, the latent heat of vaporization of water is 2.42 106 J/kg. 8

Liquid nitrogen boils at a chilly 195.8 C when the pressure is one atmosphere. A silver coin of mass 1.5 102 kg and temperature 25 C is dropped into the boiling liquid. What mass of nitrogen boils off as the coin cools to 195.8 C?

A 0.200-kg piece of aluminum that has a temperature of 155 C is added to 1.5 kg of water that has a temperature of 3.0 C. At equilibrium the temperature is 0.0 C. Ignoring the container and assuming that the heat exchanged with the surroundings is negligible, determine the mass of water that has been frozen into ice.

A thick, vertical iron pipe has an inner diameter of 0.065 m. A thin aluminum disk, heated to a temperature of 85 C, has a diameter that is 3.9 105 m greater than the pipes inner diameter. The disk is laid on top of the open upper end of the pipe, perfectly centered on it, and allowed to cool. What is the temperature of the aluminum disk when the disk falls into the pipe? Ignore the temperature change of the pipe.

On a certain evening, the dew point is 14 C and the relative humidity is 50.0%. How many Celsius degrees must the temperature fall in order for the relative humidity to increase to 69%? Use the vapor pressure curve for water that accompanies Problem 75 as needed. Assume that the dew point does not change as the temperature falls.

A lead object and a quartz object each have the same initial volume. The volume of each increases by the same amount, because the temperature increases. If the temperature of the lead object increases by 4.0 C, by how much does the temperature of the quartz object increase?

If the price of electrical energy is $0.10 per kilowatt hour, what is the cost of using electrical energy to heat the water in a swimming pool (12.0 m  9.00 m  1.5 m) from 15 to 27 C?

Concrete sidewalks are always laid in sections, with gaps between each section. For example, the drawing shows three identical 2.4-m sections, the outer two of which are against immovable walls. The two identical gaps between the sections are provided so that thermal expansion will not create the thermal stress that could lead to cracks. What is the minimum gap width necessary to account for an increase in temperature of 32 C?

A constant-volume gas thermometer (see Figures 12.3 and 12.4) has a pressure of 5.00  103 Pa when the gas temperature is 0.00 C. What is the temperature (in C) when the pressure is 2.00  103 Pa?

Ice at 10.0 C and steam at 130 C are brought together at atmospheric pressure in a perfectly insulated container. After thermal equilibrium is reached, the liquid phase at 50.0 C is present. Ignoring the container and the equilibrium vapor pressure of the liquid at 50.0 C, find the ratio of the mass of steam to the mass of ice. The specific heat capacity of steam is 2020 J/(kg C).

Two grams of liquid water are at 0 C, and another two grams are at 100 C. Heat is removed from the water at 0 C, completely freezing it at 0 C. This heat is then used to vaporize some of the water at 100 C. What is the mass (in grams) of the liquid water that remains?

Multiple-Concept Example 11 deals with a situation that is similar, but not identical, to that here. When 4200 J of heat are added to a 0.15-m-long silver bar, its length increases by 4.3  10 3 m. What is the mass of the bar?

Multiple-Concept Example 4 illustrates the concepts that are pertinent to this problem. A cylindrical brass rod (cross-sectional area 1.3  10 5 m2 ) hangs vertically straight down from a ceiling. When an 860-N block is hung from the lower end of the rod, the rod stretches. The rod is then cooled such that it contracts to its original length. By how many degrees must the temperature be lowered?

Multiple-Concept Example 11 uses the same physics principles as those employed in this problem. A block of material has a mass of 130 kg and a volume of 4.6  10 2 m3 . The material has a specific heat capacity and coefficient of volume expansion, respectively, of 750 J/(kg C) and 6.4  10 5 (C) 1 . How much heat must be added to the block in order to increase its volume by 1.2  10 5 m3 ?

A wire is made by attaching two segments together, end to end. One segment is made of aluminum and the other is steel. The effective coefficient of linear expansion of the two-segment wire is 19  10 6 (C) 1 . What fraction of the length is aluminum?

An insulated container is partly filled with oil. The lid of the container is removed, 0.125 kg of water heated to 90.0 C is poured in, and the lid is replaced. As the water and the oil reach equilibrium, the volume of the oil increases by 1.20  10 5 m3 . The density of the oil is 924 kg/m3 , its specific heat capacity is 1970 J/(kg C), and its coefficient of volume expansion is 721  10 6 (C) 1 . What is the temperature when the oil and the water reach equilibrium?

A steel bicycle wheel (without the rubber tire) is rotating freely with an angular speed of 18.00 rad/s. The temperature of the wheel changes from 100.0 to 300.0 C. No net external torque acts on the wheel, and the mass of the spokes is negligible. (a) Does the angular speed increase or decrease as the wheel heats up? Why? (b) What is the angular speed at the higher temperature?

The bulk modulus of water is B 2.2  109 N/m2 . What change in pressure P (in atmospheres) is required to keep water from expanding when it is heated from 15 to 25 C?