Answer: The average thermal conductivity of the walls

Convert 3.50 3 103 cal to an equivalent number of joules. (a) 2.74 3 104 J (b) 1.47 3 104 J (c) 3.24 3 104 J (d) 5.33 3 104 J (e) 7.20 3 105 J

Ethyl alcohol has about one-half the specific heat of water. Assume equal amounts of energy are transferred by heat into equal-mass liquid samples of alcohol and water in separate insulated containers. The water rises in temperature by 25C. How much will the alcohol rise in temperature? (a) It will rise by 12C. (b) It will rise by 25C. (c) It will rise by 50C. (d) It depends on the rate of energy transfer. (e) It will not rise in temperature.

A wall made of wood 4.00 cm thick has area of 48.0 m2. If the temperature inside is 25C and the temperature outside is 14C, at what rate is thermal energy transported through the wall by conduction? (a) 82 W (b) 210 W (c) 690 W (d) 1.1 3 103 W (e) 2.1 3 103 W

If 9.30 3 105 J of energy are transferred to 2.00 kg of ice at 0C, what is the final temperature of the system? (a) 22.4C (b) 14.2C (c) 31.5C (d) 18.0C (e) 0C

How much energy is required to raise the temperature of 5.00 kg of lead from 20.0C to its melting point of 327C? (a) 4.04 3 105 J (b) 1.07 3 105 J (c) 8.15 3 104 J (d) 2.13 3 104 J (e) 1.96 3 105 J

A granite ball of radius 2.00 m and emissivity 0.450 is heated to 135C, whereas the ambient temperature is 25.0C. What is the net power radiated from the ball? (a) 425 W (b) 3.55 3 104 W (c) 145 W (d) 2.01 3 103 W (e) 2.54 3 104 W

How long would it take a 1.00 3 103 W heating element to melt 2.00 kg of ice at 220.0C, assuming all the energy is absorbed by the ice? (a) 4.19 s (b) 419 s (c) 555 min (d) 12.5 min (e) 2.00 h

Assume you are measuring the specific heat of a sample of hot metal by using a calorimeter containing water. Because your calorimeter is not perfectly insulating, energy can transfer by heat between the contents of the calorimeter and the room. To obtain the most accurate result for the specific heat of the metal, you should use water with which initial temperature? (a) slightly lower than room temperature (b) the same as room temperature (c) slightly higher than room temperature (d) whatever you like because the initial temperature makes no difference

An amount of energy is added to ice, raising its temperature from 210C to 25C. A larger amount of energy is added to the same mass of water, raising its temperature from 15C to 20C. From these results, what can we conclude? (a) Overcoming the latent heat of fusion of ice requires an input of energy. (b) The latent heat of fusion of ice delivers some energy to the system. (c) The specific heat of ice is less than that of water. (d) The specific heat of ice is greater than that of water. (e) More information is needed to draw any conclusion.

A poker is a stiff, nonflammable rod used to push burning logs around in a fireplace. Suppose it is to be made of a single material. For best functionality and safety, should the poker be made from a material with (a) high specific heat and high thermal conductivity, (b) low specific heat and low thermal conductivity, (c) low specific heat and high thermal conductivity, (d) high specific heat and low thermal conductivity, or (e) low specific heat and low density?

Star A has twice the radius and twice the absolute temperature of star B. What is the ratio of the power output of star A to that of star B? The emissivity of both stars can be assumed to be 1. (a) 4 (b) 8 (c) 16 (d) 32 (e) 64

A person shakes a sealed, insulated bottle containing coffee for a few minutes. What is the change in the temperature of the coffee? (a) a large decrease (b) a slight decrease (c) no change (d) a slight increase (e) a large increase

A certain steel railroad rail is 13 yd in length and weighs 70.0 lb/yd. How much thermal energy is required to increase the length of such a rail by 3.0 mm? Note: Assume the steel has the same specific heat as iron.

In the summer of 1958 in St. Petersburg, Florida, a new sidewalk was poured near the childhood home of one of the authors. No expansion joints were supplied, and by mid-July the sidewalk had been completely destroyed by thermal expansion and had to be replaced, this time with the important addition of expansion joints! This event is modeled here. A slab of concrete 4.00 cm thick, 1.00 m long, and 1.00 m wide is poured for a sidewalk at an ambient temperature of 25.0C and allowed to set. The slab is exposed to direct sunlight and placed in a series of such slabs without proper expansion joints, so linear expansion is prevented. (a) Using the linear expansion equation (Eq. 10.4), eliminate DL from the equation for compressive stress and strain (Eq. 9.3). (b) Use the expression found in part (a) to eliminate DT from Equation 11.3, obtaining a symbolic equation for thermal energy transfer Q. (c) Compute the mass of the concrete slab given that its density is 2.40 3 103 kg/m3. (d) Concrete has an ultimate compressive strength of 2.00 3 107 Pa, specific heat of 880 J/kg ? C, and Youngs modulus of 2.1 3 1010 Pa. How much thermal energy must be transferred to the slab to reach this compressive stress? (e) What temperature change is required? (f) If the Sun delivers 1.00 3 103 W of power to the top surface of the slab and if half the energy, on the average, is absorbed and retained, how long does it take the slab to reach the point at which it is in danger of cracking due to compressive stress?

What mass of water at 25.0C must be allowed to come to thermal equilibrium with a 1.85-kg cube of aluminum initially at 1.50 3 102C to lower the temperature of the aluminum to 65.0C? Assume any water turned to steam subsequently recondenses.

Lead pellets, each of mass 1.00 g, are heated to 200C. How many pellets must be added to 500 g of water that is initially at 20.0C to make the equilibrium temperature 25.0C? Neglect any energy transfer to or from the container.

An aluminum cup contains 225 g of water and a 40-g copper stirrer, all at 27C. A 400-g sample of silver at an initial temperature of 87C is placed in the water. The stirrer is used to stir the mixture until it reaches its final equilibrium temperature of 32C. Calculate the mass of the aluminum cup.

In a showdown on the streets of Laredo, the good guy drops a 5.00-g silver bullet at a temperature of 20.0C into a 100-cm3 cup of water at 90.0C. Simultaneously, the bad guy drops a 5.00-g copper bullet at the same initial temperature into an identical cup of water. Which one ends the showdown with the coolest cup of water in the West? Neglect any energy transfer into or away from the container.

An aluminum calorimeter with a mass of 100 g contains 250 g of water. The calorimeter and water are in thermal equilibrium at 10.0C. Two metallic blocks are placed into the water. One is a 50.0-g piece of copper at 80.0C. The other has a mass of 70.0 g and is originally at a temperature of 100C. The entire system stabilizes at a final temperature of 20.0C. (a) Determine the specific heat of the unknown sample. (b) Using the data in Table 11.1, can you make a positive identification of the unknown material? Can you identify a possible material? (c) Explain your answers for part (b).

A 1.50-kg iron horseshoe initially at 600C is dropped into a bucket containing 20.0 kg of water at 25.0C. What is the final temperature of the water horseshoe system? Ignore the heat capacity of the container and assume a negligible amount of water boils away.

A student drops two metallic objects into a 120-g steel container holding 150 g of water at 25C. One object is a 200-g cube of copper that is initially at 85C, and the other is a chunk of aluminum that is initially at 5.0C. To the surprise of the student, the water reaches a final temperature of 25C, precisely where it started. What is the mass of the aluminum chunk?

When a driver brakes an automobile, the friction between the brake drums and the brake shoes converts the cars kinetic energy to thermal energy. If a 1 500-kg automobile traveling at 30 m/s comes to a halt, how much does the temperature rise in each of the four 8.0-kg iron brake drums? (The specific heat of iron is 448 J/kg ? C.)

Equal 0.400-kg masses of lead and tin at 60.0C are placed in 1.00 kg of water at 20.0C. (a) What is the equilibrium temperature of the system? (b) If an alloy is half lead and half tin by mass, what specific heat would you anticipate for the alloy? (c) How many atoms of tin NSn are in 0.400 kg of tin, and how many atoms of lead NPb are in 0.400 kg of lead? (d) Divide the number NSn of tin atoms by the number NPb of lead atoms and compare this ratio with the specific heat of tin divided by the specific heat of lead. What conclusion can be drawn?

An unknown substance has a mass of 0.125 kg and an initial temperature of 95.0C. The substance is then dropped into a calorimeter made of aluminum containing 0.285 kg of water initially at 25.0C. The mass of the aluminum container is 0.150 kg, and the temperature of the calorimeter increases to a final equilibrium temperature of 32.0C. Assuming no thermal energy is transferred to the environment, calculate the specific heat of the unknown substance.

A 75-g ice cube at 0C is placed in 825 g of water at 25C. What is the final temperature of the mixture?

A 50-g ice cube at 0C is heated until 45 g has become water at 100C and 5.0 g has become steam at 100C. How much energy was added to accomplish the transformation?

A 100-g cube of ice at 0C is dropped into 1.0 kg of water that was originally at 80C. What is the final temperature of the water after the ice has melted?

How much energy is required to change a 40-g ice cube from ice at 210C to steam at 110C?

A 75-kg cross-country skier glides over snow as in Figure P11.29. The coefficient of friction between skis and snow is 0.20. Assume all the snow beneath her skis is at 0C and that all the internal energy generated by friction is added to snow, which sticks to her skis until it melts. How far would she have to ski to melt 1.0 kg of snow?

Into a 0.500-kg aluminum container at 20.0C is placed 6.00 kg of ethyl alcohol at 30.0C and 1.00 kg ice at 210.0C. Assume the system is insulated from its environment. (a) Identify all five thermal energy transfers that occur as the system goes to a final equilibrium temperature T. Use the form substance at XC to substance at YC. (b) Construct a table similar to the table in Example 11.5. (c) Sum all terms in the right-most column of the table and set the sum equal to zero. (d) Substitute information from the table into the equation found in part (c) and solve for the final equilibrium temperature, T.

A 40-g block of ice is cooled to 278C and is then added to 560 g of water in an 80-g copper calorimeter at a temperature of 25C. Determine the final temperature of the system consisting of the ice, water, and calorimeter. (If not all the ice melts, determine how much ice is left.) Remember that the ice must first warm to 0C, melt, and then continue warming as water. (The specific heat of ice is 0.500 cal/g ? C 5 2 090 J/kg ? C.)

When you jog, most of the food energy you burn above your basal metabolic rate (BMR) ends up as internal energy that would raise your body temperature if it were not eliminated. The evaporation of perspiration is the primary mechanism for eliminating this energy. Determine the amount of water you lose to evaporation when running for 30 minutes at a rate that uses 400 kcal/h above your BMR. (That amount is often considered to be the maximum fat-burning energy output.) The metabolism of 1 gram of fat generates approximately 9.0 kcal of energy and produces approximately 1 gram of water. (The hydrogen atoms in the fat molecule are transferred to oxygen to form water.) What fraction of your need for water will be provided by fat metabolism? (The latent heat of vaporization of water at room temperature is 2.5 3 106 J/kg.)

A high-end gas stove usually has at least one burner rated at 14 000 Btu/h. (a) If you place a 0.25-kg aluminum pot containing 2.0 liters of water at 20C on this burner, how long will it take to bring the water to a boil, assuming all the heat from the burner goes into the pot? (b) Once boiling begins, how much time is required to boil all the water out of the pot?

A 60.0-kg runner expends 300 W of power while running a marathon. Assuming 10.0% of the energy is delivered to the muscle tissue and that the excess energy is removed from the body primarily by sweating, determine the volume of bodily fluid (assume it is water) lost per hour. (At 37.0C, the latent heat of vaporization of water is 2.41 3 106 J/kg.)

Steam at 100C is added to ice at 0C. (a) Find the amount of ice melted and the final temperature when the mass of steam is 10 g and the mass of ice is 50 g. (b) Repeat with steam of mass 1.0 g and ice of mass 50 g.

The excess internal energy of metabolism is exhausted through a variety of channels, such as through radiation and evaporation of perspiration. Consider another pathway for energy loss: moisture in exhaled breath. Suppose you breathe out 22.0 breaths per minute, each with a volume of 0.600 L. Suppose also that you inhale dry air and exhale air at 37C containing water vapor with a vapor pressure of 3.20 kPa. The vapor comes from the evaporation of liquid water in your body. Model the water vapor as an ideal gas. Assume its latent heat of evaporation at 37C is the same as its heat of vaporization at 100C. Calculate the rate at which you lose energy by exhaling humid air.

A 3.00-g lead bullet at 30.0C is fired at a speed of 2.40 3 102 m/s into a large, fixed block of ice at 0C, in which it becomes embedded. (a) Describe the energy transformations that occur as the bullet is cooled. What is the final temperature of the bullet? (b) What quantity of ice melts?

A glass windowpane in a home is 0.62 cm thick and has dimensions of 1.0 m 3 2.0 m. On a certain day, the indoor temperature is 25C and the outdoor temperature is 0C. (a) What is the rate at which energy is transferred by heat through the glass? (b) How much energy is lost through the window in one day, assuming the temperatures inside and outside remain constant?

A pond with a flat bottom has a surface area of 820 m2 and a depth of 2.0 m. On a warm day, the surface water is at a temperature of 25C, while the bottom of the pond is at 12C. Find the rate at which energy is transferred by conduction from the surface to the bottom of the pond.

The thermal conductivities of human tissues vary greatly. Fat and skin have conductivities of about 0.20 W/m ? K and 0.020 W/m ? K, respectively, while other tissues inside the body have conductivities of about 0.50 W/m ? K. Assume that between the core region of the body and the skin surface lies a skin layer of 1.0 mm, fat layer of 0.50 cm, and 3.2 cm of other tissues. (a) Find the R-factor for each of these layers, and the equivalent R-factor for all layers taken together, retaining two digits. (b) Find the rate of energy loss when the core temperature is 37C and the exterior temperature is 0C. Assume that both a protective layer of clothing and an insulating layer of unmoving air are absent, and a body area of 2.0 m2.

A steam pipe is covered with 1.50-cm-thick insulating material of thermal conductivity 0.200 cal/cm ? C ? s. How much energy is lost every second when the steam is at 200C and the surrounding air is at 20.0C? The pipe has a circumference of 800 cm and a length of 50.0 m. Neglect losses through the ends of the pipe.

The average thermal conductivity of the walls (including windows) and roof of a house in Figure P11.42 is 4.8 3 1024 kW/m ? C, and their average thickness is 21.0 cm. The house is heated with natural gas, with a heat of combustion (energy released per cubic meter of gas burned) of 9 300 kcal/m3. How many cubic meters of gas must be burned each day to maintain an inside temperature of 25.0C if the outside temperature is 0.0C? Disregard surface air layers, radiation, and energy loss by heat through the ground. 5.00 m 8.00 m 10.0 m 37.0_ Figure P11.42

Consider two cooking pots of the same dimensions, each containing the same amount of water at the same initial temperature. The bottom of the first pot is made of copper, while the bottom of the second pot is made of aluminum. Both pots are placed on a hot surface having a temperature of 145C. The water in the copper-bottomed pot boils away completely in 425 s. How long does it take the water in the aluminumbottomed pot to boil away completely?

A thermopane window consists of two glass panes, each 0.50 cm thick, with a 1.0-cm-thick sealed layer of air in between. (a) If the inside surface temperature is 23C and the outside surface temperature is 0.0C, determine the rate of energy transfer through 1.0 m2 of the window. (b) Compare your answer to (a) with the rate of energy transfer through 1.0 m2 of a single 1.0-cmthick pane of glass. Disregard surface air layers.

A copper rod and an aluminum rod of equal diameter are joined end to end in good thermal contact. The temperature of the free end of the copper rod is held constant at 100C and that of the far end of the aluminum rod is held at 0C. If the copper rod is 0.15 m long, what must be the length of the aluminum rod so that the temperature at the junction is 50C?

A Styrofoam box has a surface area of 0.80 m2 and a wall thickness of 2.0 cm. The temperature of the inner surface is 5.0C, and the outside temperature is 25C. If it takes 8.0 h for 5.0 kg of ice to melt in the container, determine the thermal conductivity of the Styrofoam.

A rectangular glass window pane on a house has a width of 1.0 m, a height of 2.0 m, and a thickness of 0.40 cm. Find the energy transferred through the window by conduction in 12 hours on a day when the inside temperature of the house is 22C and the outside temperature is 2.0C. Take surface air layers into consideration.

A solar sail is made of aluminized Mylar having an emissivity of 0.03 and reflecting 97% of the light that falls on it. Suppose a sail with area 1.00 km2 is oriented so that sunlight falls perpendicular to its surface with an intensity of 1.40 3 103 W/m2. To what temperature will it warm before it emits as much energy (from both sides) by radiation as it absorbs on the sunny side? Assume the sail is so thin that the temperature is uniform and no energy is emitted from the edges. Take the environment temperature to be 0 K.

Measurements on two stars indicate that Star X has a surface temperature of 5 727C and Star Y has a surface temperature of 11 727C. If both stars have the same radius, what is the ratio of the luminosity (total power output) of Star Y to the luminosity of Star X? Both stars can be considered to have an emissivity of 1.0.

The filament of a 75-W light bulb is at a temperature of 3 300 K. Assuming the filament has an emissivity e 5 1.0, find its surface area.

The bottom of a copper kettle has a 10-cm radius and is 2.0 mm thick. The temperature of the outside surface is 102C, and the water inside the kettle is boiling at 1 atm of pressure. Find the rate at which energy is being transferred through the bottom of the kettle.

A family comes home from a long vacation with laundry to do and showers to take. The water heater has been turned off during the vacation. If the heater has a capacity of 50.0 gallons and a 4 800-W heating element, how much time is required to raise the temperature of the water from 20.0C to 60.0C? Assume the heater is well insulated and no water is withdrawn from the tank during that time.

A 40-g ice cube floats in 200 g of water in a 100-g copper cup; all are at a temperature of 0C. A piece of lead at 98C is dropped into the cup, and the final equilibrium temperature is 12C. What is the mass of the lead?

The surface area of an unclothed person is 1.50 m2, and his skin temperature is 33.0C. The person is located in a dark room with a temperature of 20.0C, and the emissivity of the skin is e 5 0.95. (a) At what rate is energy radiated by the body? (b) What is the significance of the sign of your answer?

A 200-g block of copper at a temperature of 90C is dropped into 400 g of water at 27C. The water is contained in a 300-g glass container. What is the final temperature of the mixture?

Liquid nitrogen has a boiling point of 77 K and a latent heat of vaporization of 2.01 3 105 J/kg. A 25-W electric heating element is immersed in an insulated vessel containing 25 L of liquid nitrogen at its boiling point. (a) Describe the energy transformations that occur as power is supplied to the heating element. (b) How many kilograms of nitrogen are boiled away in a period of 4.0 hours?

A student measures the following data in a calorimetry experiment designed to determine the specific heat of aluminum: Initial temperature of water and calorimeter: 70.0C Mass of water: 0.400 kg Mass of calorimeter: 0.040 kg Specific heat of calorimeter: 0.63 kJ/kg ? C Initial temperature of aluminum: 27.0C Mass of aluminum: 0.200 kg Final temperature of mixture: 66.3C Use these data to determine the specific heat of aluminum. Explain whether your result is within 15% of the value listed in Table 11.1.

Overall, 80% of the energy used by the body must be eliminated as excess thermal energy and needs to be dissipated. The mechanisms of elimination are radiation, evaporation of sweat (2 430 kJ/kg), evaporation from the lungs (38 kJ/h), conduction, and convection. A person working out in a gym has a metabolic rate of 2 500 kJ/h. His body temperature is 37C, and the outside temperature 24C. Assume the skin has an area of 2.0 m2 and emissivity of 0.97. (a) At what rate is his excess thermal energy dissipated by radiation? (b) If he eliminates 0.40 kg of perspiration during that hour, at what rate is thermal energy dissipated by evaporation of sweat? (c) At what rate is energy eliminated by evaporation from the lungs? (d) At what rate must the remaining excess energy be eliminated through conduction and convection?

Liquid helium has a very low boiling point, 4.2 K, as well as a very low latent heat of vaporization, 2.00 3 104 J/kg. If energy is transferred to a container of liquid helium at the boiling point from an immersed electric heater at a rate of 10.0 W, how long does it take to boil away 2.00 kg of the liquid?

A class of 10 students taking an exam has a power output per student of about 200 W. Assume the initial temperature of the room is 20C and that its dimensions are 6.0 m by 15.0 m by 3.0 m. What is the temperature of the room at the end of 1.0 h if all the energy remains in the air in the room and none is added by an outside source? The specific heat of air is 837 J/kg ? C, and its density is about 1.3 3 1023 g/cm3.

A bar of gold (Au) is in thermal contact with a bar of silver (Ag) of the same length and area (Fig. P11.61). One end of the compound bar is maintained at 80.0C, and the opposite end is at 30.0C. Find the temperature at the junction when the energy flow reaches a steady state.

An iron plate is held against an iron wheel so that a sliding frictional force of 50 N acts between the two pieces of metal. The relative speed at which the two surfaces slide over each other is 40 m/s. (a) Calculate the rate at which mechanical energy is converted to internal energy. (b) The plate and the wheel have masses of 5.0 kg each, and each receives 50% of the internal energy. If the system is run as described for 10 s and each object is then allowed to reach a uniform internal temperature, what is the resultant temperature increase?

An automobile has a mass of 1 500 kg, and its aluminum brakes have an overall mass of 6.00 kg. (a) Assuming all the internal energy transformed by friction when the car stops is deposited in the brakes and neglecting energy transfer, how many times could the car be braked to rest starting from 25.0 m/s before the brakes would begin to melt? (Assume an initial temperature of 20.0C.) (b) Identify some effects that are neglected in part (a), but are likely to be important in a more realistic assessment of the temperature increase of the brakes.

Three liquids are at temperatures of 10C, 20C, and 30C, respectively. Equal masses of the first two liquids are mixed, and the equilibrium temperature is 17C. Equal masses of the second and third are then mixed, and the equilibrium temperature is 28C. Find the equilibrium temperature when equal masses of the first and third are mixed.

A flow calorimeter is an apparatus used to measure the specific heat of a liquid. The technique is to measure the temperature difference between the input and output points of a flowing stream of the liquid while adding energy at a known rate. (a) Start with the equations Q 5 mc(DT) and m 5 rV, and show that the rate at which energy is added to the liquid is given by the expression DQ /Dt 5 rc(DT)(DV/Dt). (b) In a particular experiment, a liquid of density 0.72 g/cm3 flows through the calorimeter at the rate of 3.5 cm3/s. At steady state, a temperature difference of 5.8C is established between the input and output points when energy is supplied at the rate of 40 J/s. What is the specific heat of the liquid?

A wood stove is used to heat a single room. The stove is cylindrical in shape, with a diameter of 40.0 cm and a length of 50.0 cm, and operates at a temperature of 400F. (a) If the temperature of the room is 70.0F, determine the amount of radiant energy delivered to the room by the stove each second if the emissivity is 0.920. (b) If the room is a square with walls that are 8.00 ft high and 25.0 ft wide, determine the R-value needed in the walls and ceiling to maintain the inside temperature at 70.0F if the outside temperature is 32.0F. Note that we are ignoring any heat conveyed by the stove via convection and any energy lost through the walls (and windows!) via convection or radiation.

A solar cooker consists of a curved reflecting mirror that focuses sunlight onto the object to be heated (Fig. P11.67). The solar power per unit area reaching the Earth at the location of a 0.50-m-diameter solar cooker is 600 W/m2. Assuming 50% of the incident energy is converted to thermal energy, how long would it take to boil away 1.0 L of water initially at 20C? (Neglect the specific heat of the container.)

For bacteriological testing of water supplies and in medical clinics, samples must routinely be incubated for 24 h at 37C. A standard constant-temperature bath with electric heating and thermostatic control is not suitable in developing nations without continuously operating electric power lines. Peace Corps volunteer and MIT engineer Amy Smith invented a low-cost, lowmaintenance incubator to fill the need. The device con- sists of a foam-insulated box containing several packets of a waxy material that melts at 37.0C, interspersed among tubes, dishes, or bottles containing the test samples and growth medium (food for bacteria). Outside the box, the waxy material is first melted by a stove or solar energy collector. Then it is put into the box to keep the test samples warm as it solidifies. The heat of fusion of the phase-change material is 205 kJ/kg. Model the insulation as a panel with surface area 0.490 m2, thickness 9.50 cm, and conductivity 0.012 0 W/mC. Assume the exterior temperature is 23.0C for 12.0 h and 16.0C for 12.0 h. (a) What mass of the waxy material is required to conduct the bacteriological test? (b) Explain why your calculation can be done without knowing the mass of the test samples or of the insulation.

The surface of the Sun has a temperature of about 5 800 K. The radius of the Sun is 6.96 3 108 m. Calculate the total energy radiated by the Sun each second. Assume the emissivity of the Sun is 0.986.

The evaporation of perspiration is the primary mechanism for cooling the human body. Estimate the amount of water you will lose when you bake in the sun on the beach for an hour. Use a value of 1 000 W/m2 for the intensity of sunlight and note that the energy required to evaporate a liquid at a particular temperature is approximately equal to the sum of the energy required to raise its temperature to the boiling point and the latent heat of vaporization (determined at the boiling point).

At time t 5 0, a vessel contains a mixture of 10 kg of water and an unknown mass of ice in equilibrium at 0C. The temperature of the mixture is measured over a period of an hour, with the following results: During the first 50 min, the mixture remains at 0C; from 50 min to 60 min, the temperature increases steadily from 0C to 2C. Neglecting the heat capacity of the vessel, determine the mass of ice that was initially placed in it. Assume a constant power input to the container.

An ice-cube tray is filled with 75.0 g of water. After the filled tray reaches an equilibrium temperature 20.0C, it is placed in a freezer set at 28.00C to make ice cubes. (a) Describe the processes that occur as energy is being removed from the water to make ice. (b) Calculate the energy that must be removed from the water to make ice cubes at 28.00C.

An aluminum rod and an iron rod are joined end to end in good thermal contact. The two rods have equal lengths and radii. The free end of the aluminum rod is maintained at a temperature of 100C, and the free end of the iron rod is maintained at 0C. (a) Determine the temperature of the interface between the two rods. (b) If each rod is 15 cm long and each has a cross-sectional area of 5.0 cm2, what quantity of energy is conducted across the combination in 30 min?