An engine operating at maximum theoretical efficiency

Problem 1CQ Rub your hands together vigorously. What happens? Discuss the energy transfers and transformations that take place.

Problem 1P A 10% efficient engine accelerates a 1500 kg car from rest to 15 m/s. How much energy is transferred to the engine by burning gasoline?

Problem 2CQ Write a few sentences describing the energy transformations that occur from the time moving water enters a hydroelectric plant until you see some water being pumped out of a nozzle in a public fountain. Use the “Energy transformations” table on page 324 as an example.

Problem 2P A 60% efficient device uses chemical energy to generate 600 J of electric energy. a. How much chemical energy is used? b. A second device uses twice as much chemical energy to generate half as much electric energy. What is its efficiency?

Problem 3CQ Describe the energy transfers and transformations that occur from the time you sit down to breakfast until you’ve completed a fast bicycle ride.

Problem 3P A typical photovoltaic cell delivers of electric energy when illuminated with of light energy. What is the efficiency of the

Problem 4CQ According to Table 11.4 , cycling at 15 km/h requires less metabolic energy than running at 15 km/h. Suggest reasons why this is the case.

Problem 4P An individual white LED (light-emitting diode) has an efficiency of 20% and uses 1.0 W of electric power. How many LEDs must be combined into one light source to give a total of 1.6 W of visible-light output (comparable to the light output of a 40 W incandescent bulb)? What total power is necessary to run this LED light source?

Problem 5CQ You’re stranded on a remote desert island with only a chicken, a bag of corn, and a shade tree. To survive as long as possible in hopes of being rescued, should you eat the chicken at once and then the corn? Or eat the corn, feeding enough to the chicken to keep it alive, and then eat the chicken when the corn is gone? Or are your survival chances the same either way? Explain.

Problem 6CQ For most automobiles, the number of miles per gallon decreases as highway speed increases. Fuel economy drops as speeds increase from 55 to 65 mph, then decreases further as speeds increase to 75 mph. Explain why this is the case.

Problem 5P A fast-food hamburger (with cheese and bacon) contains 1000 Calories. What is the burger’s energy in joules?

Problem 6P In an average human, basic life processes require energy to be supplied at a steady rate of 100 W. What daily energy intake, in Calories, is required to maintain these basic processes?

Problem 7CQ When the space shuttle returns to earth, its surfaces get very hot as it passes through the atmosphere at high speed. a. Has the space shuttle been heated? If so, what was the source of the heat? If not, why is it hot? b. Energy must be conserved. What happens to the space shuttle’s initial kinetic energy?

Problem 7P An “energy bar” contains 6.0 g of fat. How much energy is this in joules? In calories? In Calories?

Problem 8P An “energy bar” contains 22 g of carbohydrates. How much energy is this in joules? In calories? In Calories?

Problem 8CQ One end of a short aluminum rod is in a campfire and the other end is in a block of ice, as shown in Figure Q11.8 . If 100 J of energy are transferred from the fire to the rod, and if the temperature at every point in the rod has reached a steady value, how much energy goes from the rod into the ice?

Problem 9CQ Two blocks of copper, one of mass 1 kg and the second of mass 3 kg, are at the same temperature. Which block has more thermal energy? If the blocks are placed in thermal contact, will the thermal energy of the blocks change? If so, how?

Problem 9P An “energy bar” contains 22 g of carbohydrates. If the energy bar was his only fuel, how far could a 68 kg person walk at 5.0 km/h?

Problem 10CQ If the temperature T of an ideal gas doubles, by what factor does the average kinetic energy of the atoms change?

Problem 10P Suppose your body was able to use the chemical energy in gasoline. How far could you pedal a bicycle at 15 km/h on the energy in 1 gal of gas? (1 gal of gas has a mass of 3.2 kg.)

Problem 11CQ A bottle of helium gas and a bottle of argon gas contain equal numbers of atoms at the same temperature. Which bottle, if either, has the greater total thermal energy?

Problem 12CQ For Question, give a specific example of a process that has the energy changes and transfers described. (For example, if the question states you are to describe a process that has an increase in thermal energy and no transfer of energy by work. You could write “Heating a pan of water on the stove.”)

Problem 11P The label on a candy bar says 400 Calories. Assuming a typical efficiency for energy use by the body, if a 60 kg person were to use the energy in this candy bar to climb stairs, how high could she go?

Problem 12P A weightlifter curls a 30 kg bar, raising it each time a distance of 0.60 m. How many times must he repeat this exercise to burn off the energy in one slice of pizza?

Problem 13CQ For Question, give a specific example of a process that has the energy changes and transfers described. (For example, if the question states you are to describe a process that has an increase in thermal energy and no transfer of energy by work. You could write “Heating a pan of water on the stove.”)

Problem 13P A weightlifter works out at the gym each day. Part of her routine is to lie on her back and lift a 40 kg barbell straight up from chest height to full arm extension, a distance of 0.50 m. a. How much work does the weightlifter do to lift the barbell one time? b. If the weightlifter does 20 repetitions a day, what total energy does she expend on lifting, assuming a typical efficiency for energy use by the body. c. How many 400 Calorie donuts can she eat a day to supply that energy?

Problem 14CQ For Question, give a specific example of a process that has the energy changes and transfers described. (For example, if the question states you are to describe a process that has an increase in thermal energy and no transfer of energy by work. You could write “Heating a pan of water on the stove.”)

Problem 14P The planet Mercury’s surface temperature varies from 700 K during the day to 90 K at night. What are these values in °C and °F?

Problem 15CQ For Question, give a specific example of a process that has the energy changes and transfers described. (For example, if the question states you are to describe a process that has an increase in thermal energy and no transfer of energy by work. You could write “Heating a pan of water on the stove.”)

Problem 15P An ideal gas is at 20°C. If we double the average kinetic energy of the gas atoms, what is the new temperature in °C?

Problem 16CQ For Question, give a specific example of a process that has the energy changes and transfers described. (For example, if the question states you are to describe a process that has an increase in thermal energy and no transfer of energy by work. You could write “Heating a pan of water on the stove.”)

Problem 16P An ideal gas is at 20°C. The gas is cooled, reducing the thermal energy by 10%. What is the new temperature in °C?

Problem 17CQ For Question, give a specific example of a process that has the energy changes and transfers described. (For example, if the question states you are to describe a process that has an increase in thermal energy and no transfer of energy by work. You could write “Heating a pan of water on the stove.”)

Problem 17P An ideal gas at 0°C consists of 1.0 × 1023 atoms. 10 J of thermal energy are added to the gas. What is the new temperature in °C?

Problem 18CQ A fire piston—an impressive physics demonstration—ignites a fire without matches. The operation is shown in Figure Q11.18 . A wad of cotton is placed at the bottom of a sealed syringe with a tight-fitting plunger. When the plunger is rapidly depressed, the air temperature in the syringe rises enough to ignite the cotton. Explain why the air temperature rises, and why the plunger must be pushed in very quickly.

Problem 18P An ideal gas at 20°C consists of 2.2 × 1022 atoms. 4.3 J of thermal energy are removed from the gas. What is the new temperature in °C?

Problem 19CQ In a gasoline engine, fuel vapors are ignited by a spark. In a diesel engine, a fuel–air mixture is drawn in, then rapidly compressed to as little as 1/20 the original volume, in the process increasing the temperature enough to ignite the fuel–air mixture. Explain why the temperature rises during the compression.

Problem 19P 500 J of work are done on a system in a process that decreases the system’s thermal energy by 200 J. How much energy is transferred to or from the system as heat?

Problem 20CQ A drop of green ink falls into a beaker of clear water. First describe what happens. Then explain the outcome in terms of entropy.

Problem 20P 600 J of heat energy are transferred to a system that does 400 J of work. By how much does the system’s thermal energy change?

Problem 21CQ If you hold a rubber band loosely between two fingers and then stretch it, you can tell by touching it to the sensitive skin of your forehead that stretching the rubber band has increased its temperature. If you then let the rubber band rest against your forehead, it soon returns to its original temperature. What are the sig

Problem 21P 300 J of energy are transferred to a system in the form of heat while the thermal energy increases by 150 J. How much work is done on or by the system?

Problem 22P 10 J of heat are removed from a gas sample while it is being compressed by a piston that does 20 J of work. What is the change in the thermal energy of the gas? Does the temperature of the gas increase or decrease?

Problem 22CQ In areas in which the air temperature drops very low in the winter, the exterior unit of a heat pump designed for heating is sometimes buried underground in order to use the earth as a thermal reservoir. Why is it worthwhile to bury the heat exchanger, even if the underground unit costs more to purchase and install than one above ground?

Problem 23CQ Assuming improved materials and better processes, can engineers ever design a heat engine that exceeds the maximum efficiency indicated by Equation 11.10 ? If not, why not?

Problem 23P A heat engine extracts 55 kJ from the hot reservoir and exhausts 40 kJ into the cold reservoir. What are (a) the work done and (b) the efficiency?

Problem 24CQ Electric vehicles increase speed by using an electric motor that draws energy from a battery. When the vehicle slows, the motor runs as a generator, recharging the battery. Explain why this means that an electric vehicle can be more efficient than a gasoline-fueled vehicle.

Problem 24P A heat engine does 20 J of work while exhausting 30 J of waste heat. What is the engine’s efficiency?

Problem 25CQ When the sun’s light hits the earth, the temperature rises. Is there an entropy change to accompany this transformation? Explain.

Problem 25P A heat engine does 200 J of work while exhausting 600 J of heat to the cold reservoir. What is the engine’s efficiency?

Problem 26CQ When you put an ice cube tray filled with liquid water in your freezer, the water eventually becomes solid ice. The solid is more ordered than the liquid—it has less entropy. Explain how this transformation is possible without violating the second law of thermodynamics.

Problem 26P | A heat engine with an efficiency of 40% does 100 J of work. How much heat is (a) extracted from the hot reservoir and (b) exhausted into the cold reservoir?

Problem 27P a. At what cold-reservoir temperature (in °C) would an engine operating at maximum theoretical efficiency with a hot-reservoir temperature of 427°C have an efficiency of 60%? ________________ b. If another engine, operating at maximum theoretical efficiency with a hot-reservoir temperature of 400°C, has the same efficiency, what is its cold-reservoir temperature?

Problem 27CQ A company markets an electric heater that is described as 100% efficient at converting electric energy to thermal energy. Does this violate the second law of thermodynamics?

Problem 28MCQ A person is walking on level ground at constant speed. What energy transformation is taking place? A. Chemical energy is being transformed to thermal energy. B. Chemical energy is being transformed to kinetic energy. C. Chemical energy is being transformed to kinetic energy and thermal energy. D. Chemical energy and thermal energy are being transformed to kinetic energy.

Problem 28P A heat engine operating between energy reservoirs at 20°C and 600°C has 30% of the maximum possible efficiency. How much energy does this engine extract from the hot reservoir to do 1000 J of work?

Problem 29P A newly proposed device for generating electricity from the sun is a heat engine in which the hot reservoir is created by focusing sunlight on a small spot on one side of the engine. The cold reservoir is ambient air at 20°C. The designer claims that the efficiency will be 60%. What minimum hot-reservoir temperature, in °C, would be required to produce this efficiency?

Problem 29MCQ A person walks 1 km, turns around, and runs back to where he started. Compare the energy used and the power during the two segments. A. The energy used and the power are the same for both. B. The energy used while walking is greater, the power while running is greater. C. The energy used while running is greater, the power while running is greater. D. The energy used is the same for both segments, the power while running is greater.

Problem 30MCQ The temperature of the air in a basketball increases as it is pumped up. This means that A. The total kinetic energy of the air is increasing and the average kinetic energy of the molecules is decreasing. B. The total kinetic energy of the air is increasing and the average kinetic energy of the molecules is increasing. C. The total kinetic energy of the air is decreasing and the average kinetic energy of the molecules is decreasing. D. The total kinetic energy of the air is decreasing and the average kinetic energy of the molecules is increasing.

Problem 30P Converting sunlight to electricity with solar cells has an efficiency of ?15,. It’s possible to achieve a higher efficiency (though currently at higher cost) by using concentrated sunlight as the hot reservoir of a heat engine. Each dish in Figure P11.30 concentrates sunlight on one side of a heat engine, producing a hot-reservoir temperature of 650°C. The cold reservoir, ambient air, is approximately 30°C. The actual working efficiency of this device is ?30,. What is the theoretical maximum efficiency?

Problem 31MCQ The thermal energy of a container of helium gas is halved. What happens to the temperature, in kelvin? A. It decreases to one-fourth its initial value. ________________ B. It decreases to one-half its initial value. ________________ C. It stays the same. ________________ D. It increases to twice its initial value.

Problem 31P A refrigerator takes in 20 J of work and exhausts 50 J of heat. What is the refrigerator’s coefficient of performance?

Problem 32MCQ An inventor approaches you with a device that he claims will take 100 J of thermal energy input and produce 200 J of electricity. You decide not to invest your money because this device would violate A. The first law of thermodynamics. B. The second law of thermodynamics. C. Both the first and second laws of thermodynamics.

Problem 32P Air conditioners are rated by their coefficient of performance at 80°F inside temperature and 95°F outside temperature. An efficient but realistic air conditioner has a coefficient of performance of 3.2. What is the maximum possible coefficient of performance?

Problem 33MCQ While keeping your food cold, your refrigerator transfers energy from the inside to the surroundings. Thus thermal energy goes from a colder object to a warmer one. What can you say about this? A. It is a violation of the second law of thermodynamics. B. It is not a violation of the second law of thermodynamics because refrigerators can have efficiency of 100%. C. It is not a violation of the second law of thermodynamics because the second law doesn’t apply to refrigerators. D. The second law of thermodynamics applies in this situation, but it is not violated because the energy did not spontaneously go from cold to hot.

Problem 33P 50 J of work are done on a refrigerator with a coefficient of performance of 4.0. How much heat is (a) extracted from the cold reservoir and (b) exhausted to the hot reservoir?

Problem 34MCQ An electric power plant uses energy from burning coal to generate steam at 450°C. The plant is cooled by 20°C water from a nearby river. If burning coal provides 100 MJ of heat, what is the theoretical minimum amount of heat that must be transferred to the river during the conversion of heat to electric energy? A. 100 MJ B. 90 MJ C. 60 MJ D. 40 MJ

Problem 34P Find the maximum possible coefficient of performance for a heat pump used to heat a house in a northerly climate in winter. The inside is kept at 20°C while the outside is -20°C.

Problem 35MCQ A refrigerator’s freezer compartment is set at –10°C; the kitchen is 24°C. What is the theoretical minimum amount of electric energy necessary to pump 1.0 J of energy out of the freezer compartment? A. 0.89 J B. 0.87 J C. 0.13 J D. 0.11 J

Problem 35P Which, if any, of the heat engines in Figure P11.35 below violate (a) the first law of thermodynamics or (b) the second law of thermodynamics? Explain.

Problem 37P Draw all possible distinct arrangements in which three balls (labeled A, B, C) are placed into two different boxes (1 and 2), as in Figure 11.25. If all arrangements are equally likely, what is the probability that all three will be in box 1?

Problem 36P Which, if any, of the refrigerators in Figure P11.36 below violate (a) the first law of thermodynamics or (b) the second law of thermodynamics? Explain.

Problem 38GP How many slices of pizza must you eat to walk for 1.0 h at a speed of 5.0 km/h? (Assume your mass is 68 kg.)

Problem 39GP A 60 kg hiker climbs to the top of a 500-m-high hill. Ignoring the energy needed for horizontal motion and assuming a typical efficiency for energy use by the body, how many frozen burritos would be needed to fuel this climb?

Problem 40GP For how long would a 68 kg athlete have to swim at a fast crawl to use all the energy available in a typical fast-food meal of burger, fries, and a drink?

Problem 41GP a. How much metabolic energy is required for a 68 kg runner to run at a speed of 15 km/h for 20 min? b. How much metabolic energy is required for this runner to walk at a speed of 5.0 km/h for 60 min? Compare your result to your answer to part a. c. Compare your results of parts a and b to the result of Example 11.4. Of these three modes of human motion, which is the most efficient?

Problem 42GP To a good approximation, the only external force that does work on a cyclist moving on level ground is the force of air resistance. Suppose a cyclist is traveling at 15 km/h on level ground. Assume he is using 480 W of metabolic power. a. Estimate the amount of power he uses for forward motion. b. How much force must he exert to overcome the force of air resistance?

Problem 43GP The winning time for the 2005 annual race up 86 floors of the Empire State Building was 10 min and 49 s. The winner’s mass was 60 kg. a. If each floor was 3.7 m high, what was the winner’s change in gravitational potential energy? b. If the efficiency in climbing stairs is 25%, what total energy did the winner expend during the race? c. How many food Calories did the winner “burn” in the race? d. Of those Calories, how many were converted to thermal energy? e. What was the winner’s metabolic power in watts during the race up the stairs?

Problem 44GP Championship swimmers take about 22 s and about 30 arm strokes to move through the water in a 50 m freestyle race. a. From Table 11.4, a swimmer’s metabolic power is 800 W. If the efficiency for swimming is 25%, how much energy is expended moving through the water in a 50 m race? b. If half the energy is used in arm motion and half in leg motion, what is the energy expenditure per arm stroke? c. Model the swimmer’s hand as a paddle. During one arm stroke, the paddle moves halfway around a 90-cm-radius circle. If all the swimmer’s forward propulsion during an arm stroke comes from the hand pushing on the water and none from the arm (somewhat of an oversimplification), what is the average force of the hand on the water?

Problem 45GP A 68 kg hiker walks at 5.0 km/h up a 7% slope. What is the necessary metabolic power? Hint:You can model her power needs as the sum of the power to walk on level ground plus the power needed to raise her body by the appropriate amount.

Problem 46GP A 70 kg student consumes 2500 Cal each day and stays the same weight. One day, he eats 3500 Cal and, wanting to keep from gaining weight, decides to “work off” the excess by jumping up and down. With each jump, he accelerates to a speed of 3.3 m/s before leaving the ground. How many jumps must he make? Assume that the efficiency of the body in using energy is 25%.

Problem 47GP To make your workouts more productive, you can get an electrical generator that you drive with the rear wheel of your bicycle when it is mounted in a stand. a. Your laptop charger uses 75 W. What is your body’s metabolic power use while running the generator to power your laptop charger, given the typical efficiency for such tasks? Assume 100% efficiency for the generator. b. Your laptop takes 1 hour to recharge. If you run the generator for 1 hour, how much energy does your body use? Express your result in joules and in Calories.

Problem 48GP The resistance of an exercise bike is often provided by a generator; that is, the energy that you expend is used to generate electric energy, which is then dissipated. Rather than dissipate the energy, it could be used for practical purposes. a. A typical person can maintain a steady energy expenditure of 400 W on a bicycle. Assuming a typical efficiency for the body, and a generator that is 80% efficient, what useful electric power could you produce with a bicycle-powered generator? b. How many people would need to ride bicycle generators simultaneously to power a 400 W TV in the gym?

Problem 49GP Smaller mammals use proportionately more energy than larger mammals; that is, it takes more energy per gram to power a mouse than a human. A typical mouse has a mass of 20 g and, at rest, needs to consume 3.0 Cal each day for basic body processes. a. If a 68 kg human used the same energy per kg of body mass as a mouse, how much energy would be needed each day? b. What resting power does this correspond to? How much greater is this than the resting power noted in the chapter?

Problem 50GP Larger animals use proportionately less energy than smaller animals; that is, it takes less energy per kg to power an elephant than to power a human. A 5000 kg African elephant requires about 70,000 Cal for basic needs for one day. a. If a 68 kg human required the same energy per kg of body mass as an elephant, how much energy would be required each day? b. What resting power does this correspond to? How much less is this than the resting power noted in the chapter?

Problem 51GP A large horse can perform work at a steady rate of about 1 horsepower, as you might expect. a. Assuming a 25% efficiency, how many Calories would a horse need to consume to work at 1.0 hp for 1.0 h? b. Dry hay contains about 10 MJ per kg. How many kilograms of hay would the horse need to eat to perform this work?

Problem 52GP A college student is working on her physics homework in her dorm room. Her room contains a total of 6.0 × 1026 gas molecules. As she works, her body is converting chemical energy into thermal energy at a rate of 125 W. If her dorm room were an isolated system (dorm rooms can certainly feel like that) and if all of this thermal energy were transferred to the air in the room, by how much would the temperature increase in 10 min?

Problem 53GP A container holding argon atoms changes temperature by 20°C when 30 J of heat are removed. How many atoms are in the container?

Problem 54GP A heat engine with a high-temperature reservoir at 400 K has an efficiency of 0.20. What is the maximum possible temperature of the cold reservoir?

Problem 55GP An engine does 10 J of work and exhausts 15 J of waste heat. a. What is the engine’s efficiency? b. If the cold-reservoir temperature is 20°C, what is the minimum possible temperature in °C of the hot reservoir?

Problem 56GP The heat exhausted to the cold reservoir of an engine operating at maximum theoretical efficiency is two-thirds the heat extracted from the hot reservoir. What is the temperature ratio TC/TH ?

Problem 57GP An engine operating at maximum theoretical efficiency whose cold-reservoir temperature is 7°C is 40% efficient. By how much should the temperature of the hot reservoir be increased to raise the efficiency to 60%?

Problem 58GP Some heat engines can run on very small temperature differences. One manufacturer claims to have a very small heat engine that can run on the temperature difference between your hand and the air in the room. Estimate the theoretical maximum efficiency of this heat engine.

Problem 59GP The coefficient of performance of a refrigerator is 5.0. a. If the compressor uses 10 J of energy, how much heat is exhausted to the hot reservoir? b. If the hot-reservoir temperature is 27°C, what is the lowest possible temperature in °C of the cold reservoir?

Problem 60GP An engineer claims to have measured the characteristics of a heat engine that takes in 100 J of thermal energy and produces 50 J of useful work. Is this engine possible? If so, what is the smallest possible ratio of the temperatures (in kelvin) of the hot and cold reservoirs?

Problem 61GP The heat exhausted to the cold reservoir of an engine operating at maximum theoretical efficiency is two-thirds the heat extracted from the hot reservoir. What is the temperature ratio ?

Problem 63GP Each second, a nuclear power plant generates 2000 MJ of thermal energy from nuclear reactions in the reactor’s core. This energy is used to boil water and produce high-pressure steam at 300°C. The steam spins a turbine, which produces 700 MJ of electric power, then the steam is condensed and the water is cooled to 30°C before starting the cycle again. a. What is the maximum possible efficiency of the plant? b. What is the plant’s actual efficiency?

Problem 62GP A typical coal-fired power plant burns 300 metric tons of coal every hour to generate of electric energy. 1 metric ton = 1000 kg; 1 metric ton of coal has a volume of . The heat of combustion of coal is 28 MJ/kg. Assume that all heat is transferred from the fuel to the boiler and that all the work done in spinning the turbine is transformed into electric energy. a. Suppose the coal is piled up in a 10 m × 10 m room. How tall must the pile be to operate the plant for one day? b. What is the power plant’s efficiency?

Problem 64GP 250 students sit in an auditorium listening to a physics lecture. Because they are thinking hard, each is using 125 W of metabolic power, slightly more than they would use at rest. An air conditioner with a COP of 5.0 is being used to keep the room at a constant temperature. What minimum electric power must be used to operate the air conditioner?

Problem 65GP Driving on asphalt roads entails very little rolling resistance, so most of the energy of the engine goes to overcoming air resistance. But driving slowly in dry sand is another story. If a 1500 kg car is driven in sand at 5.0 m/s, the coefficient of rolling friction is 0.06. In this case, nearly all of the energy that the car uses to move goes to overcoming rolling friction, so you can ignore air drag in this problem. a. What propulsion force is needed to keep the car moving forward at a constant speed? b. What power is required for propulsion at 5.0 m/s? c. If the car gets 15 mpg when driving on sand, what is the car’s efficiency? One gallon of gasoline contains of chemical energy.

Problem 66GP Air conditioners sold in the United States are given a seasonal energy-efficiency ratio (SEER) rating that consumers can use to compare different models. A SEER rating is the ratio of heat pumped to energy input, similar to a COP but using English units, so a higher SEER rating means a more efficient model. You can determine the COP of an air conditioner by dividing the SEER rating by 3.4. For typical inside and outside temperatures when you’d be using air conditioning, estimate the theoretical maximum SEER rating of an air conditioner. (New air conditioners must have a SEER rating that exceeds 13, quite a bit less than the theoretical maximum, but there are practical issues that reduce efficiency.)

Problem 67GP The surface waters of tropical oceans are at a temperature of 27°C while water at a depth of 1200 m is at 3°C. It has been suggested these warm and cold waters could be the energy reservoirs for a heat engine, allowing us to do work or generate electricity from the thermal energy of the ocean. What is the maximum efficiency possible of such a heat engine?

Problem 68GP The light energy that falls on a square meter of ground over the course of a typical sunny day is about 20 MJ. The average rate of electric energy consumption in one house is 1.0 kW. a. On average, how much energy does one house use during each 24 h day? b. If light energy to electric energy conversion using solar cells is 15% efficient, how many square miles of land must be covered with solar cells to supply the electric energy for 250,000 houses? Assume there is no cloud cover.

Problem 69PP Kangaroo Locomotion Kangaroos have very stout tendons in their legs that can be used to store energy. When a kangaroo lands on its feet, the tendons stretch, transforming kinetic energy of motion to elastic potential energy. Much of this energy can be transformed back into kinetic energy as the kangaroo takes another hop. The kangaroo’s peculiar hopping gait is not very efficient at low speeds but is quite efficient at high speeds. Figure P11.68 shows the energy cost of human and kangaroo locomotion. The graph shows oxygen uptake (in mL/s) per kg of body mass, allowing a direct comparison between the two species. For humans, the energy used per second (i.e., power) is proportional to the speed. That is, the human curve nearly passes through the origin, so running twice as fast takes approximately twice as much power. For a hopping kangaroo, the graph of energy use has only a very small slope. In other words, the energy used per second changes very little with speed. Going faster requires very little additional power. Treadmill tests on kangaroos and observations in the wild have shown that they do not become winded at any speed at which they are able to hop. No matter how fast they hop, the necessary power is approximately the same. A person runs 1 km. How does his speed affect the total energy needed to cover this distance? A. A faster speed requires less total energy. B. A faster speed requires more total energy. C. The total energy is about the same for a fast speed and a slow speed.

Problem 70PP Kangaroo Locomotion Kangaroos have very stout tendons in their legs that can be used to store energy. When a kangaroo lands on its feet, the tendons stretch, transforming kinetic energy of motion to elastic potential energy. Much of this energy can be transformed back into kinetic energy as the kangaroo takes another hop. The kangaroo’s peculiar hopping gait is not very efficient at low speeds but is quite efficient at high speeds. Figure P11.68 shows the energy cost of human and kangaroo locomotion. The graph shows oxygen uptake (in mL/s) per kg of body mass, allowing a direct comparison between the two species. For humans, the energy used per second (i.e., power) is proportional to the speed. That is, the human curve nearly passes through the origin, so running twice as fast takes approximately twice as much power. For a hopping kangaroo, the graph of energy use has only a very small slope. In other words, the energy used per second changes very little with speed. Going faster requires very little additional power. Treadmill tests on kangaroos and observations in the wild have shown that they do not become winded at any speed at which they are able to hop. No matter how fast they hop, the necessary power is approximately the same. A kangaroo hops 1 km. How does its speed affect the total energy needed to cover this distance? A. A faster speed requires less total energy. B. A faster speed requires more total energy. C. The total energy is about the same for a fast speed and a slow speed.

Problem 71PP Kangaroo Locomotion Kangaroos have very stout tendons in their legs that can be used to store energy. When a kangaroo lands on its feet, the tendons stretch, transforming kinetic energy of motion to elastic potential energy. Much of this energy can be transformed back into kinetic energy as the kangaroo takes another hop. The kangaroo’s peculiar hopping gait is not very efficient at low speeds but is quite efficient at high speeds. Figure P11.68 shows the energy cost of human and kangaroo locomotion. The graph shows oxygen uptake (in mL/s) per kg of body mass, allowing a direct comparison between the two species. For humans, the energy used per second (i.e., power) is proportional to the speed. That is, the human curve nearly passes through the origin, so running twice as fast takes approximately twice as much power. For a hopping kangaroo, the graph of energy use has only a very small slope. In other words, the energy used per second changes very little with speed. Going faster requires very little additional power. Treadmill tests on kangaroos and observations in the wild have shown that they do not become winded at any speed at which they are able to hop. No matter how fast they hop, the necessary power is approximately the same. At a speed of 4 m/s, A. A running human is more efficient than an equal-mass hopping kangaroo. B. A running human is less efficient than an equal-mass hopping kangaroo. C. A running human and an equal-mass hopping kangaroo have about the same efficiency.

Problem 72PP Kangaroo Locomotion Kangaroos have very stout tendons in their legs that can be used to store energy. When a kangaroo lands on its feet, the tendons stretch, transforming kinetic energy of motion to elastic potential energy. Much of this energy can be transformed back into kinetic energy as the kangaroo takes another hop. The kangaroo’s peculiar hopping gait is not very efficient at low speeds but is quite efficient at high speeds. Figure P11.68 shows the energy cost of human and kangaroo locomotion. The graph shows oxygen uptake (in mL/s) per kg of body mass, allowing a direct comparison between the two species. For humans, the energy used per second (i.e., power) is proportional to the speed. That is, the human curve nearly passes through the origin, so running twice as fast takes approximately twice as much power. For a hopping kangaroo, the graph of energy use has only a very small slope. In other words, the energy used per second changes very little with speed. Going faster requires very little additional power. Treadmill tests on kangaroos and observations in the wild have shown that they do not become winded at any speed at which they are able to hop. No matter how fast they hop, the necessary power is approximately the same. At approximately what speed would a human use half the power of an equal-mass kangaroo moving at the same speed? A. 3 m/s B. 4 m/s C. 5 m/s D. 6 m/s

Problem 73PP Kangaroo Locomotion Kangaroos have very stout tendons in their legs that can be used to store energy. When a kangaroo lands on its feet, the tendons stretch, transforming kinetic energy of motion to elastic potential energy. Much of this energy can be transformed back into kinetic energy as the kangaroo takes another hop. The kangaroo’s peculiar hopping gait is not very efficient at low speeds but is quite efficient at high speeds. Figure P11.68 shows the energy cost of human and kangaroo locomotion. The graph shows oxygen uptake (in mL/s) per kg of body mass, allowing a direct comparison between the two species. For humans, the energy used per second (i.e., power) is proportional to the speed. That is, the human curve nearly passes through the origin, so running twice as fast takes approximately twice as much power. For a hopping kangaroo, the graph of energy use has only a very small slope. In other words, the energy used per second changes very little with speed. Going faster requires very little additional power. Treadmill tests on kangaroos and observations in the wild have shown that they do not become winded at any speed at which they are able to hop. No matter how fast they hop, the necessary power is approximately the same. At what speed does the hopping motion of the kangaroo become more efficient than the running gait of a human? A. 3 m/s B. 5 m/s C. 7 m/s D. 9 m/s