Solved: Your 300 mL cup of coffee is too hot to drink when

Problem 1CQ Which has more mass, a mole of Ne gas or a mole of gas?

Problem 1P Which contains the most moles: 10 g of hydrogen gas, 100 g of carbon, or 50 g of lead?

Problem 2CQ If you launch a projectile upward with a high enough speed, its kinetic energy is sufficient to allow it to escape the earth’s gravity—it will go up and not come back down. Given enough time, hydrogen and helium gas atoms in the earth’s atmosphere will escape, so these elements are not present in our atmosphere. Explain why hydrogen and helium atoms have the necessary speed to escape but why other elements, such as oxygen and nitrogen, do not.

Problem 2P How many grams of water have the same number of oxygen atoms as 1.0 mol of oxygen gas?

Problem 3P You may have noticed that latex helium balloons tend to shrink rather quickly; a balloon filled with air lasts a lot longer. Balloons shrink because gas diffuses out of them. The rate of diffusion is faster for smaller particles and for particles of higher speed. Diffusion is also faster when there is a large difference in concentration between two sides of a membrane. Given these facts, explain why an air-filled balloon lasts longer than a helium balloon.

Problem 3CQ You may have noticed that latex helium balloons tend to shrink rather quickly; a balloon filled with air lasts a lot longer. Balloons shrink because gas diffuses out of them. The rate of diffusion is faster for smaller particles and for particles of higher speed. Diffusion is also faster when there is a large difference in concentration between two sides of a membrane. Given these facts, explain why an air-filled balloon lasts longer than a helium balloon.

Problem 4CQ If you buy a sealed bag of potato chips in Miami and drive with it to Denver, where the atmospheric pressure is lower, you will find that the bag gets very “puffy.” Explain why.

Problem 4P How many cubic millimeters are in 1 L?

Problem 5CQ If you double the typical speed of the molecules in a gas, by what factor does the pressure change? Give a simple explanation why the pressure changes by this factor.

Problem 5P A box is 200 cm wide, 40 cm deep, and 3.0 cm high. What is its volume in ?

Problem 6CQ Two gases have the same number of molecules per cubic meter (N / V ) and the same rms speed. The molecules of gas 2 are more massive than the molecules of gas 1. a. Do the two gases have the same pressure? If not, which is larger? b. Do the two gases have the same temperature? If not, which is larger?

Problem 6P Dry ice is frozen carbon dioxide. If you have 1.0 kg of dry ice, what volume will it occupy if you heat it enough to turn it into a gas at a temperature of 20°C?

Problem 7CQ a. Which contains more particles, a mole of helium gas or a mole of oxygen gas? Explain. b. Which contains more particles, a gram of helium gas or a gram of oxygen gas? Explain.

Problem 7P What is the absolute pressure of the air in your car’s tires, in psi, when your pressure gauge indicates they are inflated to 35.0 psi? Assume you are at sea level.

Problem 8CQ You have 100 g of aluminum and 100 g of lead. a. Which contains a larger number of moles? Explain. ________________ b. Which contains more atoms? Explain.

Problem 8P Total lung capacity of a typical adult is approximately 5.0 L. Approximately 20% of the air is oxygen. At sea level and at an average body temperature of 37°C, how many moles of oxygen do the lungs contain at the end of an inhalation?

Problem 9CQ Suppose you could suddenly increase the speed of every atom in a gas by a factor of 2. a. Does the thermal energy of the gas change? If so, by what factor? If not, why not? ________________ b. Does the molar specific heat change? If so, by what factor? If not, why not?

Problem 9P Many cultures around the world still use a simple weapon called a blowgun, a tube with a dart that fits tightly inside. A sharp breath into the end of the tube launches the dart. When exhaling forcefully, a healthy person can supply air at a gauge pressure of 6.0 kPa. What force does this pressure exert on a dart in a 1.5-cm-diameter tube?

Problem 10CQ A gas cylinder contains 1.0 mol of helium at a temperature of 20°C. A second identical cylinder contains 1.0 mol of neon at 20°C. The helium atoms are moving with a higher average speed, but the gas pressure in the two containers is the same. Explain how this is possible.

Problem 10P When you stifle a sneeze, you can damage delicate tissues because the pressure of the air that is not allowed to escape may rise by up to 45 kPa. If this extra pressure acts on the inside of your 8.4-mm-diameter eardrum, what is the outward force?

Problem 11CQ A gas is in a sealed container. By what factor does the gas pressure change if a. The volume is doubled and the temperature is tripled? b. The volume is halved and the temperature is tripled?

Problem 11P 7.5 mol of helium are in a 15 L cylinder. The pressure gauge on the cylinder reads 65 psi. What are (a) the temperature of the gas in °C and (b) the average kinetic energy of a helium atom?

Problem 12CQ A gas is in a sealed container. By what factor does the gas temperature change if a. The volume is doubled and the pressure is tripled? b. The volume is halved and the pressure is tripled?

Problem 12P Mars has an atmosphere composed almost entirely of carbon dioxide, with an average temperature of –63°C. What is the rms speed of a molecule in Mars’s atmosphere?

Problem 13CQ What is the maximum amount of work that a gas can do during a constant-volume process?

Problem 13P 3.0 mol of gas at a temperature of -120°C fills a 2.0 L container. What is the gas pressure?

Problem 14CQ You need to precisely measure the dimensions of a large wood panel for a construction project. Your metal tape measure was left outside for hours in the sun on a hot summer day, and now the tape is so hot it’s painful to pick up. How will your measurements differ from those taken by your coworker, whose tape stayed in the shade? Explain.

Problem 14P 265 m/s is a typical cruising speed for a jet airliner. At what temperature (in °C) do the molecules of nitrogen gas have an rms speed of 265 m/s?

Problem 15CQ Your car’s radiator is made of steel and is filled with water. You fill the radiator to the very top with cold water, then drive off without remembering to replace the cap. As the water and the steel radiator heat up, will the level of water drop or will it rise and overflow? Explain.

Problem 16CQ Materials A and B have equal densities, but A has a larger specific heat than B. You have 100 g cubes of each material. Cube A, initially at 0°C, is placed in good thermal contact with cube B, initially at 200°C. The cubes are inside a well-insulated container where they don’t interact with their surroundings. Is their final temperature greater than, less than, or equal to 100°C? Explain.

Problem 15P 10 g of liquid water is placed in a flexible bag, the air is excluded, and the bag is sealed. It is then placed in a microwave oven where the water is boiled to make steam at 100°C. What is the volume of the bag after all the water has boiled? Assume that the pressure inside the bag is equal to atmospheric pressure.

Problem 16P A cylinder contains 3.0 L of oxygen at 300 K and 2.4 atm. The gas is heated, causing a piston in the cylinder to move outward. The heating causes the temperature to rise to 600 K and the volume of the cylinder to increase to 9.0 L. What is the final gas pressure?

Problem 17CQ Two containers hold equal masses of nitrogen gas at equal temperatures. You supply 10 J of heat to container A while not allowing its volume to change, and you supply 10 J of heat to container B while not allowing its pressure to change. Afterward, is temperature ? Explain.

Problem 17P

Problem 18CQ You need to raise the temperature of a gas by 10°C. To use the smallest amount of heat energy, should you heat the gas at constant pressure or at constant volume? Explain.

Problem 19CQ A sample of ideal gas is in a cylinder with a movable piston. 600 J of heat is added to the gas in an isothermal process. As the gas expands, pushing against the piston, how much work does it do?

Problem 18P 0.10 mol of argon gas is admitted to an evacuated 50 cm3 container at 20°C. The gas then undergoes heating at constant volume to a temperature of 300°C. a. What is the final pressure of the gas? b. Show the process on a pV diagram. Include a proper scale on both axes.

Problem 19P 0.10 mol of argon gas is admitted to an evacuated container at 20°C. The gas then undergoes an isobaric heating to a temperature of 300°C. a. What is the final volume of the gas? b. Show the process on a pV diagram. Include a proper scale on both axes.

Problem 20CQ A student is heating chocolate in a pan on the stove. He uses a cooking thermometer to measure the temperature of the chocolate and sees it varies as shown in Figure Q12.21 on the next page. Describe what is happening to the chocolate in each of the three portions of the graph.

Problem 20P 0.10 mol of argon gas is admitted to an evacuated container at 20°C. The gas then undergoes an isothermal expansion to a volume of . a. What is the final pressure of the gas? b. Show the process on a pV diagram. Include a proper scale on both axes.

Problem 21CQ If you bake a cake at high elevation, where atmospheric pressure is lower than at sea level, you will need to adjust the recipe. You will need to cook the cake for a longer time, and you will need to add less baking powder. (Baking powder is a leavening agent. As it heats, it releases gas bubbles that cause the cake to rise.) Explain why those adjustments are necessary.

Problem 21P 0.0040 mol of gas undergoes the process shown in Figure P12.25 . a. What type of process is this? b. What are the initial and final temperatures?

Problem 22CQ The specific heat of aluminum is higher than that of iron. 1 kg blocks of iron and aluminum are heated to 100°C, and each is then dropped into its own 1 L beaker of 20°C water. Which beaker will end up with the warmer water? Explain.

Problem 22P 0.0040 mol of gas follows the hyperbolic trajectory shown in Figure P12.26 . a. What type of process is this? b. What are the initial and final temperatures? c. What is the final volume ?

Problem 23CQ A student is asked to sketch a pV diagram for a gas that goes through a cycle consisting of (a) an isobaric expansion, (b) a constant-volume reduction in temperature, and (c) an isothermal process that returns the gas to its initial state. The student draws the diagram shown in Figure Q12.24. What, if anything, is wrong with the student’s diagram?

Problem 23P A gas with an initial temperature of 900°C undergoes the process shown in Figure P12.27 on the next page. a. What type of process is this? b. What is the final temperature? c. How many moles of gas are there?

Problem 24CQ If you have two spoons of the same size, one silver and one stainless steel, there is a quick test to tell which is which. Hold the end of a spoon in each hand, then lower them both into a cup of very hot water. One spoon will feel hot first. Is that the silver spoon or the stainless steel spoon? Explain.

Problem 24P How much work is done on the gas in the process shown in Figure P12.28?

Problem 25CQ If you live somewhere with cold, clear nights, you may have noticed some mornings when there was frost on open patches of ground but not under trees. This is because the ground under trees does not get as cold as open ground. Explain how tree cover keeps the ground under trees warmer.

Problem 25P It is possible to make a thermometer by sealing gas in a rigid container and measuring the absolute pressure. Such a constant- volume gas thermometer is placed in an ice-water bath at 0.00°C. After reaching thermal equilibrium, the gas pressure is recorded as 55.9 kPa. The thermometer is then placed in contact with a sample of unknown temperature. After the thermometer reaches a new equilibrium, the gas pressure is 65.1 kPa. What is the temperature of this sample?

Problem 26MCQ A tire is inflated to a gauge pressure of 35 psi. The absolute pressure in the tire is A. Less than 35 psi. B. Equal to 35 psi. C. Greater than 35 psi.

Problem 26P A air bubble is released from the sandy bottom of a warm, shallow sea, where the gauge pressure is 1.5 atm. The bubble rises slowly enough that the air inside remains at the same constant temperature as the water. a. What is the volume of the bubble as it reaches the surface? b. As the bubble rises, is heat energy transferred from the water to the bubble or from the bubble to the water? Explain.

Problem 27MCQ The number of atoms in a container is increased by a factor of 2 while the temperature is held constant. The pressure A. Decreases by a factor of 4. B. Decreases by a factor of 2. C. Stays the same. D. Increases by a factor of 2. E. Increases by a factor of 4.

Problem 27P A weather balloon rises through the atmosphere, its volume expanding from as the temperature drops from 20°C to –10°C. If the initial gas pressure inside the balloon is 1.0 atm, what is the final pressure?

Problem 28MCQ A gas is compressed by an isothermal process that decreases its volume by a factor of 2. In this process, the pressure A. Does not change. B. Increases by a factor of less than 2. C. Increases by a factor of 2. D. Increases by a factor of more than 2.

Problem 28P A straight rod consists of a 1.2-cm-long piece of aluminum attached to a 2.0-cm-long piece of steel. By how much will the length of this rod change if its temperature is increased from 20°C to 40°C?

Problem 29MCQ A gas is compressed by an adiabatic process that decreases its volume by a factor of 2. In this process, the pressure A. Does not change. B. Increases by a factor of less than 2. C. Increases by a factor of 2. D. Increases by a factor of more than 2.

Problem 29P The length of a steel beam increases by 0.73 mm when its temperature is raised from 22°C to 35°C. What is the length of the beam at 22°C?

Problem 30MCQ Suppose you do a calorimetry experiment to measure the specific heat of a penny. You take a number of pennies, measure their mass, heat them to a known temperature, and then drop them into a container of water at a known temperature. You then deduce the specific heat of a penny by measuring the temperature change of the water. Unfortunately, you didn’t realize that you dropped one penny on the floor while transferring them to the water. This will A. Cause you to underestimate the specific heat. B. Cause you to overestimate the specific heat. C. Not affect your calculation of specific heat.

Problem 30P Older railroad tracks in the U.S. are made of 12-m-long pieces of steel. When the tracks are laid, gaps are left between the sections to prevent buckling when the steel thermally expands. If a track is laid at 16°C, how large should the gaps be if the track is not to buckle when the temperature is as high as 50°C?

Problem 31MCQ Acup of water is heated with a heating coil that delivers 100 W of heat. In one minute, the temperature of the water rises by 20°C. What is the mass of the water? A. 72 g B. 140 g C. 720 g D. 1.4 kg

Problem 31P The temperature of an aluminum disk is increased by 120°C. By what percentage does its volume increase?

Problem 32MCQ Three identical beakers each hold 1000 g of water at 20°C. 100 g of liquid water at 0°C is added to the first beaker, 100 g of ice at 0°C is added to the second beaker, and the third beaker gets 100 g of aluminum at 0°C. The contents of which container end up at the lowest final temperature? A. The first beaker. B. The second beaker. C. The third beaker. D. All end up at the same temperature.

Problem 32P How much energy must be removed from a 200 g block of ice to cool it from 0°C to -30°C?

Problem 33MCQ 100 g of ice at 0°C and 100 g of steam at 100°C interact thermally in a well-insulated container. The final state of the system is A. An ice-water mixture at 0°C. B. Water at a temperature between 0°C and 50°C. C. Water at 50°C. D. Water at a temperature between 50°C and 100°C. E. A water-steam mixture at 100°C.

Problem 34MCQ Suppose the 600 W of radiation emitted in a microwave oven is absorbed by 250 g of water in a very lightweight cup. Approximately how long will it take to heat the water from 20°C to 80°C? A. 50 s B. 100 s C. 150 s D. 200 s

Problem 33P How much heat is needed to change 20 g of mercury at 20°C into mercury vapor at the boiling point?

Problem 34P a. 100 J of heat energy are transferred to 20 g of mercury initially at 20°C. By how much does the temperature increase? b. How much heat is needed to raise the temperature of 20 g of water by the same amount?

Problem 35MCQ 40,000 J of heat is added to 1.0 kg of ice at -10°C. How much ice melts? A. 0.012 kg B. 0.057 kg C. 0.12 kg D. 1.0 kg

Problem 35P The maximum amount of water an adult in temperate climates can perspire in one hour is typically 1.8 L. However, after several weeks in a tropical climate the body can adapt, increasing the maximum perspiration rate to 3.5 L/h. At what rate, in watts, is energy being removed when perspiring that rapidly? Assume all of the perspired water evaporates. At body temperature, the heat of vaporization of water is .

Problem 36MCQ Steam at 100°C causes worse burns than liquid water at 100°C. This is because A. The steam is hotter than the water. B. Heat is transferred to the skin as steam condenses. C. Steam has a higher specific heat than water. D. Evaporation of liquid water on the skin causes cooling.

Problem 36P Alligators and other reptiles don’t use enough metabolic energy to keep their body temperatures constant. They cool off at night and must warm up in the sun in the morning. Suppose a 300 kg alligator with an earlymorning body temperature of 25°C is absorbing radiation from the sun at a rate of 1200 W. How long will the alligator need to warm up to a more favorable 30°C? (Assume that the specific heat of the reptilian body is the same as that of the mammalian body.)

Problem 37P When air is inhaled, it quickly becomes saturated with water vapor as it passes through the moist upper airways. When a person breathes dry air, about 25 mg of water are exhaled with each breath. At 12 breaths/min, what is the rate of energy loss due to evaporation? Express your answer in both watts and Calories per day. At body temperature, the heat of vaporization of water is .

Problem 38P It is important for the body to have mechanisms to effectively cool itself; if not, moderate exercise could easily increase body temperatures to dangerous levels. Suppose a 70 kg man runs on a treadmill for 30 min, using a metabolic power of 1000 W. Assume that all of this power goes to thermal energy in the body. If he couldn’t perspire or otherwise cool his body, by how much would his body temperature rise during this exercise?

Problem 39P What minimum heat is needed to bring 100 g of water at 20°C to the boiling point and completely boil it away?

Problem 40P 30 g of copper pellets are removed from a 300°C oven and immediately dropped into 100 mL of water at 20°C in an insulated cup. What will the new water temperature be?

Problem 41P A copper block is removed from a 300°C oven and dropped into 1.00 kg of water at 20.0°C. The water quickly reaches 25.5°C and then remains at that temperature. What is the mass of the copper block?

Problem 42P A 750 g aluminum pan is removed from the stove and plunged into a sink filled with 10.0 kg of water at 20.0°C. The water temperature quickly rises to 24.0°C. What was the initial temperature of the pan?

Problem 44P Brewed coffee is often too hot to drink right away. You can cool it with an ice cube, but this dilutes it. Or you can buy a device that will cool your coffee without dilution—a 200 g aluminum cylinder that you take from your freezer and place in a mug of hot coffee. If the cylinder is cooled to –20°C, a typical freezer temperature, and then dropped into a large cup of coffee (essentially water, with a mass of 500 g) at 85°C, what is the final temperature of the coffee?

Problem 43P A 500 g metal sphere is heated to 300°C, then dropped into a beaker containing 4.08 kg of mercury at 20.0°C. A short time later the mercury temperature stabilizes at 99.0°C. Identify the metal.

Problem 45P Marianne really likes coffee, but on summer days she doesn’t want to drink a hot beverage. If she is served 200 mL of coffee at 80°C in a well-insulated container, how much ice at 0°C should she add to obtain a final temperature of 30°C?

Problem 46P If a person has a dangerously high fever, submerging her in ice water is a bad idea, but an ice pack can help to quickly bring her body temperature down. How many grams of ice at 0°C will be melted in bringing down a 60 kg patient’s fever from 40°C to 39°C?

Problem 48P A container holds 1.0 g of oxygen at a pressure of 8.0 atm. a. How much heat is required to increase the temperature by 100°C at constant pressure? b. How much will the temperature increase if this amount of heat energy is transferred to the gas at constant volume?

Problem 47P A container holds 1.0 g of argon at a pressure of 8.0 atm. a. How much heat is required to increase the temperature by 100°C at constant volume? b. How much will the temperature increase if this amount of heat energy is transferred to the gas at constant pressure?

Problem 49P What is the temperature change of 1.0 mol of a monatomic gas if its thermal energy is increased by 1.0 J?

Problem 50P The temperature of 2.0 g of helium is increased at constant volume by ?T. What mass of oxygen can have its temperature increased by the same amount at constant volume using the same amount of heat?

Problem 51P How much work is done per cycle by a gas following the pV trajectory of Figure 51? FIGURE 51

Problem 52P A gas folio wing the pV trajectory of Figure 52 does 60 J of work per cycle. What is pmax? FIGURE 52

Problem 53P A 1.8-cm-thick wood floor covers a 4.0 m × 5.5 m room. The subfloor on which the flooring sits is at a temperature of 16.2°C, while the air in the room is at 19.6°C. What is the rate of heat conduction through the floor?

Problem 54P A copper-bottomed kettle, its bottom 24 cm in diameter and 3.0 mm thick, sits on a burner. The kettle holds boiling water, and energy flows into the water from the kettle bottom at 800 W. What is the temperature of the bottom surface of the kettle?

Problem 55P What is the greatest possible rate of energy transfer by radiation from a metal cube 2.0 cm on a side that is at 700°C? Its emissivity is 0.20.

Problem 56P What is the greatest possible rate of energy transfer by radiation for a 5.0-cm-diameter sphere that is at 100°C?

Problem 57P Seals may cool themselves by using thermal windows, patches on their bodies with much higher than average surface temperature. Suppose a seal has a thermal window at a temperature of 30°C. If the seal’s surroundings are a frosty -10°C, what is the net rate of energy loss by radiation? Assume an emissivity equal to that of a human.

Problem 58P Electronics and inhabitants of the International Space Station generate a significant amount of thermal energy that the station must get rid of. The only way that the station can exhaust thermal energy is by radiation, which it does using thin, 1.8-m-by- 3.6-m panels that have a working temperature of about 6°C. How much power is radiated from each panel? Assume that the panels are in the shade so that the absorbed radiation will be negligible. Assume that the emissivity of the panels is 1.0. Hint: Don’t forget that the panels have two sides!

Problem 59P The glowing filament in a lamp is radiating energy at a rate of 60 W. At the filament’s temperature of 1500°C, the emissivity is 0.23. What is the surface area of the filament?

Problem 60P If you lie on the ground at night with no cover, you get cold rather quickly. Much of this is due to energy loss by radiation. At night in a dry climate, the temperature of the sky can drop to -40°C. If you are lying on the ground with thin clothing that provides little insulation, the surface temperature of your skin and clothes will be about 30°C. Estimate the net rate at which your body loses energy by radiation to the night sky under these conditions. Hint: What area should you use?

Problem 61GP A rigid container holds 2.0 mol of gas at a pressure of 1.0 atm and a temperature of 30°C. a. What is the container’s volume? b. What is the pressure if the temperature is raised to 130°C?

Problem 62GP A 15-cm-diameter compressed-air tank is 50 cm tall. The pressure at 20°C is 150 atm. a. How many moles of air are in the tank? b. What volume would this air occupy at STP?

Problem 63GP A 10-cm-diameter cylinder of helium gas is 30 cm long and at 20°C. The pressure gauge reads 120 psi. a. How many helium atoms are in the cylinder? b. What is the mass of the helium?

Problem 64GP Party stores sell small tanks containing 30 g of helium gas. If you use such a tank to fill 0.010 m3 foil balloons (which don’t stretch, and so have an internal pressure that is very close to atmospheric pressure), how many balloons can you expect to fill?

Problem 65GP Suppose you take and hold a deep breath on a chilly day, inhaling 3.0 L of air at 0°C. Assume that the pressure in your lungs is constant at 1.0 atm. a. How much heat must your body supply to warm the air to your internal body temperature of 37°C? b. How much does the air’s volume increase as it is warmed?

Problem 66GP On average, each person in the industrialized world is responsible for the emission of 10,000 kg of carbon dioxide every year. This includes that you generate directly, by burning fossil fuels to operate your car or your furnace, as well as generated on your behalf by electric generating stations and manufacturing plants. is a greenhouse gas that contributes to global warming. If you were to store your yearly emissions in a cube at STP, how long would each edge of the cube be?

Problem 67GP On a cool morning, when the temperature is 15°C, you measure the pressure in your car tires to be 30 psi. After driving 20 mi on the freeway, the temperature of your tires is 45°C. What pressure will your tire gauge now show?

Problem 68GP Suppose you inflate your car tires to 35 psi on a 20°C day. Later, the temperature drops to 0°C. What is the pressure in your tires now?

Problem 69GP The volume in a constant-pressure gas thermometer is directly proportional to the absolute temperature. A constant-pressure thermometer is calibrated by adjusting its volume to 1000 mL while it is in contact with a reference cell at 0.01°C. The volume increases to 1638 mL when the thermometer is placed in contact with a sample. What is the sample’s temperature in °C?

Problem 70GP A compressed-air cylinder is known to fail if the pressure exceeds 110 atm. A cylinder that was filled to 25 atm at 20°C is stored in a warehouse. Unfortunately, the warehouse catches fire and the temperature reaches 950°C. Does the cylinder explode?

Problem 71GP A rigid sphere has a valve that can be opened or closed. The sphere with the valve open is placed in boiling water in a room where the air pressure is 1.0 atm. After a long period of time has elapsed, the valve is closed. What will be the pressure inside the sphere if it is then placed in (a) a mixture of ice and water and (b) an insulated box filled with dry ice, which is at ?78.5°C?

Problem 72GP 80 J of work are done on the gas in the process shown in Figure P12.81. What is ?

Problem 73GP How much work is done by the gas in the process shown in Figure P12.82?

Prolem 74GP 0.10 mol of gas undergoes the process 1? 2 shown in Figure P12.83. a. What are temperatures ? b. What type of process is this? c. The gas undergoes constant-volume heating from point 2 until the pressure is restored to the value it had at point 1. What is the final temperature of the gas?

Problem 75GP 10 g of dry ice (solid ) is placed in a container, then all the air is quickly pumped out and the container sealed. The container is warmed to 0°C, a temperature at which is a gas. a. What is the gas pressure? Give your answer in atm. The gas then undergoes an isothermal compression until the pressure is 3.0 atm, immediately followed by an isobaric compression until the volume is . b. What is the final temperature of the gas? c. Show the process on a pV diagram.

Problem 76GP A large freshwater fish has a swim bladder with a volume of . The fish descends from a depth where the absolute pressure is 3.0 atm to deeper water where the swim bladder is compressed to 60% of its initial volume. As the fish descends, the gas pressure in the swim bladder is always equal to the water pressure, and the temperature of the gas remains at the internal temperature of the fish’s body. To adapt to its new location, the fish must add gas to reinflate its swim bladder to the original volume. This takes energy to accomplish. What’s the minimum amount of work required to expand the swim bladder back to its original volume?

Problem 77GP A 5.0-m-diameter garden pond holds of water. Solar energy is incident on the pond at an average rate of . If the water absorbs all the solar energy and does not exchange energy with its surroundings, how many hours will it take to warm from 15°C to 25°C?

Problem 78GP 0.030 mol of an ideal monatomic gas undergoes an adiabatic compression that raises its temperature from 10°C to 50°C. How much work is done on the gas to compress it?

Problem 79GP 0.15 mol of an ideal monatomic gas undergoes an adiabatic expansion, cooling from 20°C to ?10°C. How much work is done by the gas during the expansion?

Problem 80GP Susan, whose mass is 68 kg, climbs 59 m to the top of the Cape Hatteras lighthouse. a. During the climb, by how much does her potential energy increase? b. For a typical efficiency of 25%, what metabolic energy does she require to complete the climb? c. When exercising, the body must perspire and use other mechanisms to cool itself to avoid potentially dangerous increases on body temperature. If we assume that Susan doesn’t perspire or otherwise cool herself and that all of the “lost” energy goes into increasing her body temperature, by how much would her body temperature increase during this climb?

Problem 81GP A typical nuclear reactor generates 1000 MW of electric energy. In doing so, it produces “waste heat” at a rate of 2000 MW, and this heat must be removed from the reactor. Many reactors are sited next to large bodies of water so that they can use the water for cooling. Consider a reactor where the intake water is at 18°C. State regulations limit the temperature of the output water to 30°C so as not to harm aquatic organisms. How many kilograms of cooling water have to be pumped through the reactor each minute?

Problem 82GP A 68 kg woman cycles at a constant 15 km/h. All of the metabolic energy that does not go to forward propulsion is converted to thermal energy in her body. If the only way her body has to keep cool is by evaporation, how many kilograms of water must she lose to perspiration each hour to keep her body temperature constant?

Problem 83GP A 1200 kg car traveling at 60 mph quickly brakes to a halt. The kinetic energy of the car is converted to thermal energy of the disk brakes. The brake disks (one per wheel) are iron disks with a mass of 4.0 kg. Estimate the temperature rise in each disk as the car stops.

Problem 84GP A 5000 kg African elephant has a resting metabolic rate of 2500 W. On a hot day, the elephant’s environment is likely to be nearly the same temperature as the animal itself, so cooling by radiation is not effective. The only plausible way to keep cool is by evaporation, and elephants spray water on their body to accomplish this. If this is the only possible means of cooling, how many kilograms of water per hour must be evaporated from an elephant’s skin to keep it at a constant temperature?

Problem 85GP Suppose you drop a water balloon from a height of 10 m. If the balloon doesn’t break on impact, its kinetic energy will be converted to thermal energy. Estimate the temperature rise of the water. Is this likely to be noticeable?

Problem 86GP What is the maximum mass of lead you could melt with 1000 J of heat, starting from 20°C?

Problem 87GP An experiment measures the temperature of a 200 g substance while steadily supplying heat to it. Figure P12.95 shows the results of the experiment. What are (a) the specific heat of the liquid phase and (b) the heat of vaporization?

Problem 88GP 10 g of aluminum at 200°C and 20 g of copper are dropped into of ethyl alcohol at 15°C. The temperature quickly comes to 25°C. What was the initial temperature of the copper?

Problem 89GP A 100 g ice cube at -10°C is placed in an aluminum cup whose initial temperature is 70°C. The system comes to an equilibrium temperature of 20°C. What is the mass of the cup?

Problem 90GP A 50.0 g thermometer is used to measure the temperature of 200 g of water. The specific heat of the thermometer, which is mostly glass, is 750 J/kg · K, and it reads 20.0°C while lying on the table. After being completely immersed in the water, the thermometer’s reading stabilizes at 71.2°C. What was the actual water temperature before it was measured?

Problem 91GP Your 300 mL cup of coffee is too hot to drink when served at 90°C. What is the mass of an ice cube, taken from a -20°C freezer, that will cool your coffee to a pleasant 60°C?

Problem 92GP A gas is compressed from at a constant pressure of 400 kPa. At the same time, 100 J of heat energy is transferred out of the gas. What is the change in thermal energy of the gas during this process?

Problem 93GP An expandable cube, initially 20 cm on each side, contains 3.0 g of helium at 20°C. 1000 J of heat energy are transferred to this gas. What are (a) the final pressure if the process is at constant volume and (b) the final volume if the process is at constant pressure?

Problem 94GP 0.10 mol of a monatomic gas follows the process shown in Figure P12.102. a. How much heat energy is transferred to or from the gas during process 1? 2? b. How much heat energy is transferred to or from the gas during process 2? 3? c. What is the total change in thermal energy of the gas?

Problem 95GP A monatomic gas follows the process 1? 2? 3 shown in Figure P12.103. How much heat is needed for (a) process 1? 2 and (b) process 2? 3

Problem 97GP The top layer of your goose down sleeping bag has a thickness of 5.0 cm and a surface area of . When the outside temperature is -20°C, you lose 25 Cal/h by heat conduction through the bag (which remains at a cozy 35°C inside). Assume that you’re sleeping on an insulated pad that eliminates heat conduction to the ground beneath you. What is the thermal conductivity of the goose down?

Problem 96GP What are (a) the heat extracted from the hot reservoir and (b) the efficiency for a heat engine described by the pV diagram of Figure P12.104?

Problem 98GP Suppose you go outside in your fiber-filled jacket on a windless but very cold day. The thickness of the jacket is 2.5 cm, and it covers of your body. The purpose of fiber- or down-filled jackets is to trap a layer of air, and it’s really the air layer that provides the insulation. If your skin temperature is 34°C while the air temperature is -20°C, at what rate is heat being conducted through the jacket and away from your body?

Problem 99GP Two thin, square copper plates are radiating energy at the same rate. The edge length of plate 2 is four times that of plate 1. What is the ratio of absolute temperatures T1 /T2of the plates?

Problem 100GP The surface area of an adult human is about . Suppose a person with a skin temperature of 34°C is standing with bare skin in a room where the air is 25°C but the walls are 17°C. a. There is a “dead-air” layer next to your skin that acts as insulation. If the dead-air layer is 5.0 mm thick, what is the person’s rate of heat loss by conduction? b. What is the person’s net radiation loss to the walls? The emissivity of skin is 0.97. c. Does conduction or radiation contribute more to the total rate of energy loss? d. If the person is metabolizing food at a rate of 155 W, does the person feel comfortable, chilly, or too warm?

Problem 101PP Thermal Properties of the Oceans Seasonal temperature changes in the ocean only affect the top layer of water, to a depth of 500 m or so. This “mixed” layer is thermally isolated from the cold, deep water below. The average temperature of this top layer of the world’s oceans, which has area , is approximately 17°C. In addition to seasonal temperature changes, the oceans have experienced an overall warming trend over the last century that is expected to continue as the earth’s climate changes. A warmer ocean means a larger volume of water; the oceans will rise. Suppose the average temperature of the top layer of the world’s oceans were to increase from a temperature . The area of the oceans will not change, as this is fixed by the size of the ocean basin, so any thermal expansion of the water will cause the water level to rise, as shown in Figure P12.109. The original volume is the product of the original depth and the surface area, . The change in volume is given by ?V = A ?d. If the top 500 m of ocean water increased in temperature from 17°C to 18°C, what would be the resulting rise in ocean height? A. 0.11 m B. 0.22 m C. 0.44 m D. 0.88 m

Problem 102PP Thermal Properties of the Oceans Seasonal temperature changes in the ocean only affect the top layer of water, to a depth of 500 m or so. This “mixed” layer is thermally isolated from the cold, deep water below. The average temperature of this top layer of the world’s oceans, which has area , is approximately 17°C. In addition to seasonal temperature changes, the oceans have experienced an overall warming trend over the last century that is expected to continue as the earth’s climate changes. A warmer ocean means a larger volume of water; the oceans will rise. Suppose the average temperature of the top layer of the world’s oceans were to increase from a temperature . The area of the oceans will not change, as this is fixed by the size of the ocean basin, so any thermal expansion of the water will cause the water level to rise, as shown in Figure P12.109. The original volume is the product of the original depth and the surface area, . The change in volume is given by ?V = A ?d. Approximately how much energy would be required to raise the temperature of the top layer of the oceans by 1°C? ( of water has a mass of 1000 kg.)

Problem 103PP Thermal Properties of the Oceans Seasonal temperature changes in the ocean only affect the top layer of water, to a depth of 500 m or so. This “mixed” layer is thermally isolated from the cold, deep water below. The average temperature of this top layer of the world’s oceans, which has area , is approximately 17°C. In addition to seasonal temperature changes, the oceans have experienced an overall warming trend over the last century that is expected to continue as the earth’s climate changes. A warmer ocean means a larger volume of water; the oceans will rise. Suppose the average temperature of the top layer of the world’s oceans were to increase from a temperature . The area of the oceans will not change, as this is fixed by the size of the ocean basin, so any thermal expansion of the water will cause the water level to rise, as shown in Figure P12.109. The original volume is the product of the original depth and the surface area, . The change in volume is given by ?V = A ?d. Water’s coefficient of expansion varies with temperature. For water at 2°C, an increase in temperature of 1°C would cause the volume to A. Increase. B. Stay the same. C. Decrease.

Problem 104PP Thermal Properties of the Oceans Seasonal temperature changes in the ocean only affect the top layer of water, to a depth of 500 m or so. This “mixed” layer is thermally isolated from the cold, deep water below. The average temperature of this top layer of the world’s oceans, which has area , is approximately 17°C. In addition to seasonal temperature changes, the oceans have experienced an overall warming trend over the last century that is expected to continue as the earth’s climate changes. A warmer ocean means a larger volume of water; the oceans will rise. Suppose the average temperature of the top layer of the world’s oceans were to increase from a temperature . The area of the oceans will not change, as this is fixed by the size of the ocean basin, so any thermal expansion of the water will cause the water level to rise, as shown in Figure P12.109. The original volume is the product of the original depth and the surface area, . The change in volume is given by ?V = A ?d. The ocean is mostly heated from the top, by light from the sun. The warmer surface water doesn’t mix much with the colder deep ocean water. This lack of mixing can be ascribed to a lack of A. Conduction. B. Convection. C. Radiation. D. Evaporation.