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physics
college physics 2nd
College Physics 2nd Edition OpenStax - Solutions
Suppose you stand with one foot on ceramic flooring and one foot on a wool carpet, making contact over an area of 80.0 cm2 with each foot. Both the ceramic and the carpet are 2.00 cm thick and are 10.0°C on their bottom sides. At what rate must heat transfer occur from each foot to keep the top of
(a) A firewalker runs across a bed of hot coals without sustaining burns. Calculate the heat transferred by conduction into the sole of one foot of a firewalker given that the bottom of the foot is a 3.00-mm-thick callus with a conductivity at the low end of the range for wood and its density is
(a) What is the rate of heat conduction through the 3.00-cm-thick fur of a large animal having a 1.40-m2 surface area? Assume that the animal's skin temperature is 32.0°C, that the air temperature is -5.00°C, and that fur has the same thermal conductivity as air. (b) What food intake will the
A walrus transfers energy by conduction through its blubber at the rate of 150 W when immersed in -1.00°C water. The walrus's internal core temperature is 37.0°C, and it has a surface area of 2.00 m2. What is the average thickness of its blubber, which has the conductivity of fatty tissues
Some stove tops are smooth ceramic for easy cleaning. If the ceramic is 0.600 cm thick and heat conduction occurs through the same area and at the same rate as computed in Example 14.6, what is the temperature difference across it? Ceramic has the same thermal conductivity as glass and brick.Data
Suppose a person is covered head to foot by wool clothing with average thickness of 2.00 cm and is transferring energy by conduction through the clothing at the rate of 50.0 W. What is the temperature difference across the clothing, given the surface area is 1.40 m2?
One easy way to reduce heating (and cooling) costs is to add extra insulation in the attic of a house. Suppose the house already had 15 cm of fiberglass insulation in the attic and in all the exterior surfaces. If you added an extra 8.0 cm of fiberglass to the attic, then by what percentage would
(a) Calculate the rate of heat conduction through a double-paned window that has a 1.50-m2 area and is made of two panes of 0.800-cm-thick glass separated by a 1.00-cm air gap. The inside surface temperature is 15.0°C, while that on the outside is -10.0°C.(b) Calculate the rate of heat conduction
Many decisions are made on the basis of the payback period: the time it will take through savings to equal the capital cost of an investment. Acceptable payback times depend upon the business or philosophy one has. (For some industries, a payback period is as small as two years.) Suppose you wish
For the human body, what is the rate of heat transfer by conduction through the body's tissue with the following conditions: the tissue thickness is 3.00 cm, the change in temperature is 2.00°C, and the skin area is 1.50 m2. How does this compare with the average heat transfer rate to the body
At what wind speed does -10°C air cause the same chill factor as still air at -29°C?
Does still air cause the same At what temperature chill factor as -5°C air moving at 15 m/s?
The "steam" above a freshly made cup of instant coffee is really water vapor droplets condensing after evaporating from the hot coffee. What is the final temperature of 250 g of hot coffee initially at 90.0°C if 2.00 g evaporates from it? The coffee is in a Styrofoam cup, so other methods of heat
(a) How many kilograms of water must evaporate from a 60.0-kg woman to lower her body temperature by 0.750°C? (b) Is this a reasonable amount of water to evaporate in the form of perspiration, assuming the relative humidity of the surrounding air is low?
On a hot dry day, evaporation from a lake has just enough heat transfer to balance the 1.00 kW/m2 of incoming heat from the Sun. What mass of water evaporates in 1.00 h from each square meter? Explicitly show how you follow the steps in the Problem-Solving Strategies for the Effects of Heat
The Kilauea volcano in Hawaii is the world's most active, disgorging about 5 x 105 m of 1200°C lava per day. What is the rate of heat transfer out of Earth by convection if this lava has a density of 2700 kg/m3 and eventually cools to 30°C? Assume that the specific heat of lava is the same as
During heavy exercise, the body pumps 2.00 L of blood per minute to the surface, where it is cooled by 2.00°C. What is the rate of heat transfer from this forced convection alone, assuming blood has the same specific heat as water and its density is 1050 kg/m3?
A person inhales and exhales 2.00 L of 37.0°C air, evaporating 4.00 x 10-2 g of water from the lungs and breathing passages with each breath.(a) How much heat transfer occurs due to evaporation in each breath?(b) What is the rate of heat transfer in watts if the person is breathing at a moderate
A glass coffee pot has a circular bottom with a 9.00-cm diameter in contact with a heating element that keeps the coffee warm with a continuous heat transfer rate of 50.0 W(a) What is the temperature of the bottom of the pot, if it is 3.00 mm thick and the inside temperature is 60.0°C? (b) If the
At what net rate does heat radiate from a 275-m2 black roof on a night when the roof's temperature is 30.0°C and the surrounding temperature is 15.0°C? The emissivity of the roof is 0.900.
(a) Cherry-red embers in a fireplace are at 850°C and have an exposed area of 0.200 m2 and an emissivity of 0.980. The surrounding room has a temperature of 18.0°C. If 50% of the radiant energy enters the room, what is the net rate of radiant heat transfer in kilowatts?(b) Does your answer
Radiation makes it impossible to stand close to a hot lava flow. Calculate the rate of heat transfer by radiation from 1.00 m2 of 1200°C fresh lava into 30.0°C surroundings, assuming lava's emissivity is 1.00.
Find the net rate of heat transfer by radiation from a skier standing in the shade, given the following. She is completely clothed in white (head to foot, including a ski mask), the clothes have an emissivity of 0.200 and a surface temperature of 10.0°C, the surroundings are at -15.0°C, and her
Suppose you walk into a sauna that has an ambient temperature of 50.0°C.(a) Calculate the rate of heat transfer to you by radiation given your skin temperature is 37.0°C, the emissivity of skin is 0.98, and the surface area of your body is 1.50 m2. (b) If all other forms of heat transfer are
The Sun radiates like a perfect black body with an emissivity of exactly 1. (a) Calculate the surface temperature of the Sun, given that it is a sphere with a 7.00 × 108-m radius that radiates 3.80 x 1026 W into 3-K space. (b) How much power does the Sun radiate per square meter of its
A large body of lava from a volcano has stopped flowing and is slowly cooling. The interior of the lava is at 1200°C, its surface is at 450°C, and the surroundings are at 27.0°C.(a) Calculate the rate at which energy is transferred by radiation from 1.00 m2 of surface lava into the surroundings,
Calculate the temperature the entire sky would have to be in order to transfer energy by radiation at 1000 W/m2 -about the rate at which the Sun radiates when it is directly overhead on a clear day. This value is the effective temperature of the sky, a kind of average that takes account of the fact
One 30.0°C day the relative humidity is 75.0%, and that evening the temperature drops to 20.0°C, well below the dew point.(a) How many grams of water condense from each cubic meter of air? (b) How much heat transfer occurs by this condensation? (c) What temperature increase could this cause in
Large meteors sometimes strike the Earth, converting most of their kinetic energy into thermal energy.(a) What is the kinetic energy of a 109 kg meteor moving at 25.0 km/s?(b) If this meteor lands in a deep ocean and 80% of its kinetic energy goes into heating water, how many kilograms of water
Frozen waste from airplane toilets has sometimes been accidentally ejected at high altitude. Ordinarily it breaks up and disperses over a large area, but sometimes it holds together and strikes the ground. Calculate the mass of 0°C ice that can be melted by the conversion of kinetic and
(a) A large electrical power facility produces 1600 MW of "waste heat," which is dissipated to the environment in cooling towers by warming air flowing through the towers by 5.00°C. What is the necessary flow rate of air in m3/s? (b) Is your result consistent with the large cooling towers used by
A 76.0-kg person suffering from hypothermia comes indoors and shivers vigorously. How long does it take the heat transfer to increase the person's body temperature by 2.00°C if all other forms of heat transfer are balanced?
In certain large geographic regions, the underlying rock is hot. Wells can be drilled and water circulated through the rock for heat transfer for the generation of electricity.(a) Calculate the heat transfer that can be extracted by cooling 1.00 km3 of granite by 100°C. (b) How long will this
Heat transfers from your lungs and breathing passages by evaporating water.(a) Calculate the maximum number of grams of water that can be evaporated when you inhale 1.50 L of 37°C air with an original relative humidity of 40.0%. (Assume that body temperature is also 37°C.) (b) How many joules of
(a) What is the temperature increase of water falling 55.0 m over Niagara Falls? (b) What fraction must evaporate to keep the temperature constant?
Hot air rises because it has expanded. It then displaces a greater volume of cold air, which increases the buoyant force on it.(a) Calculate the ratio of the buoyant force to the weight of 50.0°C air surrounded by 20.0°C air. (b) What energy is needed to cause 1.00 m3 of air to go from 20.0°C
An Arctic inventor surrounded by ice thinks it would be much less mechanically complex to cool a car engine by melting ice on it than by having a water-cooled system with a radiator, water pump, antifreeze, and so on.(a) If 80.0% of the energy in 1.00 gal of gasoline is converted into "waste heat"
(a) Calculate the rate of heat transfer by conduction through a window with an area of 1.00 m2 that is 0.750 cm thick, if its inner surface is at 22.0°C and its outer surface is at 35.0°C. (b) What is unreasonable about this result? (c) Which premise or assumption is responsible?
A meteorite 1.20 cm in diameter is so hot immediately after penetrating the atmosphere that it radiates 20.0 kW of power. (a) What is its temperature, if the surroundings are at 20.0°C and it has an emissivity of 0.800? (b) What is unreasonable about this result?(c) Which premise or assumption
Consider a new model of commercial airplane having its brakes tested as a part of the initial flight permission procedure. The airplane is brought to takeoff speed and then stopped with the brakes alone. Construct a problem in which you calculate the temperature increase of the brakes during this
Consider a person outdoors on a cold night. Construct a problem in which you calculate the rate of heat transfer from the person by all three heat transfer methods. Make the initial circumstances such that at rest the person will have a net heat transfer and then decide how much physical activity
How much heat transfer occurs from a system, if its internal energy decreased by 150 J while it was doing 30.0 J of work?
A system does 1.80 x 108 J of work while 7.50 x 108 J of heat transfer occurs to the environment. What is the change in internal energy of the system assuming no other changes (such as in temperature or by the addition of fuel)?
What is the change in internal energy of a system which does 4.50 x 105 J of work while 3.00 × 106 J of heat transfer occurs into the system, and 8.00 × 106 J of heat transfer occurs to the environment?
Suppose a woman does 500 J of work and 9500 J of heat transfer occurs into the environment in the process. (a) What is the decrease in her internal energy, assuming no change in temperature or consumption of food? (That is, there is no other energy transfer.) (b) What is her efficiency?
(a) How much food energy will a man metabolize in the process of doing 35.0 kJ of work with an efficiency of 5.00%? (b) How much heat transfer occurs to the environment to keep his temperature constant? Explicitly show how you follow the steps in the Problem-Solving Strategy for thermodynamics
(a) How long will the energy in a 1470-kJ (350-kcal) cup of yogurt last in a woman doing work at the rate of 150 W with an efficiency of 20.0% (such as in leisurely climbing stairs)? (b) Does the time found in part (a) imply that it is easy to consume more food energy than you can reasonably
(a) A woman climbing the Washington Monument metabolizes 6.00 × 102 kJ of food energy. If her efficiency is 18.0%, how much heat transfer occurs to the environment to keep her temperature constant? (b) Discuss the amount of heat transfer found in (a). Is it consistent with the fact that you
A car tire contains 0.0380 m3 of nitrogen at a gauge pressure of 2.20 x 105 N/m2 (about 32 psi). How much more internal energy does this gas have than the same volume has at zero gauge pressure (which is equivalent to normal atmospheric pressure)? (Use U = 5/2 NkT for the internal energy of
A helium-filled rigid ball has a gauge pressure of 0.200 atm and a volume of 10.0 L. How much greater is the internal energy of the helium in the ball than it would be at zero gauge pressure?
Steam to drive an old-fashioned steam locomotive is supplied at a constant gauge pressure of 1.75 × 106 N/m2 (about 250 psi) to a piston with a 0.200-m radius.(a) By calculating PΔV, find the work done by the steam when the piston moves 0.800 m. Note that this is the net work output, since gauge
Calculate the net work output of a heat engine following path ABCDA in the figure below. P (106 N/m²) 2.6 2.0 1.0 0.6 A D 1.0 B C 4.0 V (10-³ m³)
A hand-driven tire pump has a piston with a 2.50-cm diameter and a maximum stroke of 30.0 cm. (a) How much work do you do in one stroke if the average gauge pressure is 2.40 x 105 N/m2 (about 35 psi)?(b) What average force do you exert on the piston, neglecting friction and gravitational force?
What is the net work output of a heat engine that follows path ABDA in the figure above, with a straight line from B to D? Why is the work output less than for path ABCDA? Explicitly show how you follow the steps in the Problem-Solving Strategies for Thermodynamics.
What is wrong with the claim that a cyclical heat engine does 4.00 kJ of work on an input of 24.0 kJ of heat transfer while 16.0 kJ of heat transfers to the environment?
(a) A cyclical heat engine, operating between temperatures of 450°C and 150°C produces 4.00 MJ of work on a heat transfer of 5.00 MJ into the engine. How much heat transfer occurs to the environment?(b) What is unreasonable about the engine? (c) Which premise is unreasonable?
Consider a car’s gasoline engine. Construct a problem in which you calculate the maximum efficiency this engine can have. Among the things to consider are the effective hot and cold reservoir temperatures. Compare your calculated efficiency with the actual efficiency of car engines.
Consider a car trip into the mountains. Construct a problem in which you calculate the overall efficiency of the car for the trip as a ratio of kinetic and potential energy gained to fuel consumed. Compare this efficiency to the thermodynamic efficiency quoted for gasoline engines and discuss why
A certain heat engine does 10.0 kJ of work and 8.50 kJ of heat transfer occurs to the environment in a cyclical process.(a) What was the heat transfer into this engine? (b) What was the engine’s efficiency?
(a) What is the work output of a cyclical heat engine having a 22.0% efficiency and 6.00 × 109 J of heat transfer into the engine? (b) How much heat transfer occurs to the environment?
(a) What is the efficiency of a cyclical heat engine in which 75.0 kJ of heat transfer occurs to the environment for every 95.0 kJ of heat transfer into the engine? (b) How much work does it produce for 100 kJ of heat transfer into the engine?
The engine of a large ship does 2.00 × 108 J of work with an efficiency of 5.00%.(a) How much heat transfer occurs to the environment? (b) How many barrels of fuel are consumed, if each barrel produces 6.00 × 109 J of heat transfer when burned?
(a) How much heat transfer occurs to the environment by an electrical power station that uses 1.25x1014 J of heat transfer into the engine with an efficiency of 42.0% ? (b) What is the ratio of heat transfer to the environment to work output? (c) How much work is done?
Assume that the turbines at a coal-powered power plant were upgraded, resulting in an improvement in efficiency of 3.32%. Assume that prior to the upgrade the power station had an efficiency of 36% and that the heat transfer into the engine in one day is still the same at 2.50 x 1014 J. (a) How
This problem compares the energy output and heat transfer to the environment by two different types of nuclear power stations-one with the normal efficiency of 34.0%, and another with an improved efficiency of 40.0%. Suppose both have the same heat transfer into the engine in one day, 2.50x1014
A gas-cooled nuclear reactor operates between hot and cold reservoir temperatures of 700°C and 27.0°C.(a) What is the maximum efficiency of a heat engine operating between these temperatures?(b) Find the ratio of this efficiency to the Carnot efficiency of a standard nuclear reactor (found in
A certain gasoline engine has an efficiency of 30.0%. What would the hot reservoir temperature be for a Carnot engine having that efficiency, if it operates with a cold reservoir temperature of 200°C?
(a) What is the hot reservoir temperature of a Carnot engine that has an efficiency of 42.0% and a cold reservoir temperature of 27.0°C?(b) What must the hot reservoir temperature be for a real heat engine that achieves 0.700 of the maximum efficiency, but still has an efficiency of 42.0% (and a
Steam locomotives have an efficiency of 17.0% and operate with a hot steam temperature of 425°C.(a) What would the cold reservoir temperature be if this were a Carnot engine? (b) What would the maximum efficiency of this steam engine be if its cold reservoir temperature were 150°C?
Practical steam engines utilize 450°C steam, which is later exhausted at 270°C.(a) What is the maximum efficiency that such a heat engine can have? (b) Since 270°C steam is still quite hot, a second steam engine is sometimes operated using the exhaust of the first. What is the maximum
A coal-fired electrical power station has an efficiency of 38%. The temperature of the steam leaving the boiler is 550°C. What percentage of the maximum efficiency does this station obtain? (Assume the temperature of the environment is 20°C.)
Would you be willing to financially back an inventor who is marketing a device that she claims has 25 kJ of heat transfer at 600 K, has heat transfer to the environment at 300 K, and does 12 kJ of work? Explain your answer.
(a) Suppose you want to design a steam engine that has heat transfer to the environment at 270°C and has a Carnot efficiency of 0.800. What temperature of hot steam must you use? (b) What is unreasonable about the temperature? (c) Which premise is unreasonable?
What is the coefficient of performance of an ideal heat pump that has heat transfer from a cold temperature of -25.0°C to a hot temperature of 40.0°C?
Suppose you have an ideal refrigerator that cools an environment at -20.0°C and has heat transfer to another environment at 50.0°C. What is its coefficient of performance?
What is the best coefficient of performance possible for a hypothetical refrigerator that could make liquid nitrogen at -200°C and has heat transfer to the environment at 35.0°C?
In a very mild winter climate, a heat pump has heat transfer from an environment at 5.00°C to one at 35.0°C. What is the best possible coefficient of performance for these temperatures? Explicitly show how you follow the steps in the Problem-Solving Strategies for Thermodynamics.
(a) What is the best coefficient of performance for a heat pump that has a hot reservoir temperature of 50.0°C and a cold reservoir temperature of -20.0°C? (b) How much heat transfer occurs into the warm environment if 3.60 x 107 J of work (10.0kW h) is put into it? (c) If the cost of this work
Suppose you want to operate an ideal refrigerator with a cold temperature of -10.0°C, and you would like it to have a coefficient of performance of 7.00. What is the hot reservoir temperature for such a refrigerator?
An ideal heat pump is being considered for use in heating an environment with a temperature of 22.0°C. What is the cold reservoir temperature if the pump is to have a coefficient of performance of 12.0?
A 4-ton air conditioner removes 5.06 x 107 J (48,000 British thermal units) from a cold environment in 1.00 h. (a) What energy input in joules is necessary to do this if the air conditioner has an energy efficiency rating (EER) of 12.0? (b) What is the cost of doing this if the work costs 10.0
Show that the coefficients of performance of refrigerators and heat pumps are related by COPref = COPhp - 1. Start with the definitions of the COPs and the conservation of energy relationship between Qh, Qc, and W.
On a hot summer day, 4.00 × 106 J of heat transfer into a parked car takes place, increasing its temperature from 35.0°C to 45.0°C. What is the increase in entropy of the car due to this heat transfer alone?
A hot rock ejected from a volcano's lava fountain cools from 1100°C to 40.0°C, and its entropy decreases by 950 J/K. How much heat transfer occurs from the rock?
When 1.60 × 105 J of heat transfer occurs into a meat pie initially at 20.0°C, its entropy increases by 480 J/K. What is its final temperature?
The Sun radiates energy at the rate of 3.80 × 1026 W from its 5500°C surface into dark empty space (a negligible fraction radiates onto Earth and the other planets). The effective temperature of deep space is -270°C. (a) What is the increase in entropy in one day due to this heat transfer? (b)
(a) In reaching equilibrium, how much heat transfer occurs from 1.00 kg of water at 40.0°C when it is placed in contact with 1.00 kg of 20.0°C water in reaching equilibrium? (b) What is the change in entropy due to this heat transfer? (c) How much work is made unavailable, taking the lowest
Find the increase in entropy of 1.00 kg of liquid nitrogen that starts at its boiling temperature, boils, and warms to 20.0°C at constant pressure.
A large electrical power station generates 1000 MW of electricity with an efficiency of 35.0%. (a) Calculate the heat transfer to the power station, Qh, in one day. (b) How much heat transfer Qc occurs to the environment in one day? (c) If the heat transfer in the cooling towers is from 35.0°C
Using Table 15.4, verify the contention that if you toss 100 coins each second, you can expect to get 100 heads or 100 tails once in 2 × 1022 years; calculate the time to two-digit accuracy.Data given in Table 15.4 Macrostate Heads Tails 100 99 95 90 75 60 55 51 50 0 1 LO 10 25 40 45 49 50 Number
(a) How much heat transfer occurs from 20.0 kg of 90.0°C water placed in contact with 20.0 kg of 10.0°C water, producing a final temperature of 50.0°C? (b) How much work could a Carnot engine do with this heat transfer, assuming it operates between two reservoirs at constant temperatures of
What percent of the time will you get something in the range from 60 heads and 40 tails through 40 heads and 60 tails when tossing 100 coins? The total number of microstates in that range is 1.22 x 1030. (Consult Table 15.4.)Data given in Table 15.4 Macrostate Heads
(a) What is the change in entropy if you start with 10 coins in the 5 heads and 5 tails macrostate, toss them, and get 2 heads and 8 tails? (b) How much more likely is 5 heads and 5 tails than 2 heads and 8 tails? (Take the ratio of the number of microstates to find out.) (c) If you were betting
(a) If you toss 10 coins, what percent of the time will you get the three most likely macrostates (6 heads and 4 tails, 5 heads and 5 tails, 4 heads and 6 tails)? (b) You can realistically toss 10 coins and count the number of heads and tails about twice a minute. At that rate, how long will it
(a) Construct a table showing the macrostates and all of the individual microstates for tossing 6 coins. (Use Table 15.5 as a guide.) (b) How many macrostates are there? (c) What is the total number of microstates? (d) What percent chance is there of tossing 5 heads and 1 tail? (e) How much
(a) What is the change in entropy if you start with 100 coins in the 45 heads and 55 tails macrostate, toss them, and get 51 heads and 49 tails? (b) What if you get 75 heads and 25 tails?(c) How much more likely is 51 heads and 49 tails than 75 heads and 25 tails?(d) Does either outcome violate
In an air conditioner, 12.65 MJ of heat transfer occurs from a cold environment in 1.00 h. (a) What mass of ice melting would involve the same heat transfer? (b) How many hours of operation would be equivalent to melting 900 kg of ice? (c) If ice costs 20 cents per kg, do you think the air
Explain why a building made of bricks has smaller entropy than the same bricks in a disorganized pile. Do this by considering the number of ways that each could be formed (the number of microstates in each macrostate).
If you place 0°C ice into 0°C water in an insulated container, what will happen? Will some ice melt, will more water freeze, or will neither take place?
What effect does condensation on a glass of ice water have on the rate at which the ice melts? Will the condensation speed up the melting process or slow it down?
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