Fundamentals of Physics 8th Extended edition Jearl Walker, Halliday Resnick - Solutions

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One of the most efficient heat engines ever built is a steam turbine in the Ohio valley, operating between 430°C and 1 870°C on energy from West Virginia coal to produce electricity for the Midwest. (a) What is its maximum theoretical efficiency? (b) The actual efficiency of the engine is
A heat engine operating between 200°C and 80.0°C achieves 20.0% of the maximum possible efficiency. What energy input will enable the engine to perform 10.0 kJ of work?
An ideal gas is taken through a Carnot cycle. The isothermal expansion occurs at 250°C, and the isothermal compression takes place at 50.0°C. The gas takes in 1 200 J of energy from the hot reservoir during the isothermal expansion. Find (a) The energy expelled to the cold reservoir in each
The exhaust temperature of a Carnot heat engine is 300°C. What is the intake temperature if the efficiency of the engine is 30.0%?
A Carnot heat engine uses a steam boiler at 100°C as the high-temperature reservoir. The low-temperature reservoir is the outside environment at 20.0°C. Energy is exhausted to the low-temperature reservoir at the rate of 15.4 W. (a) Determine the useful power output of the heat engine. (b) How
A power plant operates at a 32.0% efficiency during the summer when the sea water used for cooling is at 20.0°C. The plant uses 350°C steam to drive turbines. If the plant’s efficiency changes in the same proportion as the ideal efficiency, what would be the plant’s efficiency in the winter,
Argon enters a turbine at a rate of 80.0 kg/min, a temperature of 800°C and a pressure of 1.50 MPa. It expands adiabatically as it pushes on the turbine blades and exits at pressure 300 kPa. (a) Calculate its temperature at exit. (b) Calculate the (maximum) power output of the turning turbine.
An electric power plant that would make use of the temperature gradient in the ocean has been proposed. The system is to operate between 20.0°C (surface water temperature) and 5.00°C (water temperature at a depth of about 1 km). (a) What is the maximum efficiency of such a system? (b) If the
Here is a clever idea. Suppose you build a two-engine device such that the exhaust energy output from one heat engine is the input energy for a second heat engine. We say that the two engines are running in series. Let e 1 and e 2 represent the efficiencies of the two engines. (a) The overall
A 20.0%-efficient real engine is used to speed up a train from rest to 5.00 m/s. It is known that an ideal (Carnot) engine using the same cold and hot reservoirs would accelerate the same train from rest to a speed of 6.50 m/s using the same amount of fuel. The engines use air at 300 K as a cold
A firebox is at 750 K, and the ambient temperature is 300 K. The efficiency of a Carnot engine doing 150 J of work as it transports energy between these constant-temperature baths is 60.0%. The Carnot engine must take in energy 150 J/0.600 = 250 J from the hot reservoir and must put out 100 J of
At point A in a Carnot cycle, 2.34 mol of a monatomic ideal gas has a pressure of 1 400 kPa, a volume of 10.0 L, and a temperature of 720 K. It expands isothermally to point B, and then expands adiabatically to point C where its volume is 24.0 L. An isothermal compression brings it to point D,
What is the coefficient of performance of a refrigerator that operates with Carnot efficiency between temperatures "3.00°C and &27.0°C?
What is the maximum possible coefficient of performance of a heat pump that brings energy from outdoors at "3.00°C into a 22.0°C house? Note that the work done to run the heat pump is also available to warm up the house.
An ideal refrigerator or ideal heat pump is equivalent to a Carnot engine running in reverse. That is, energy Q c is taken in from a cold reservoir and energy Q h is rejected to a hot reservoir. (a) Show that the work that must be supplied to run the refrigerator or heat pump is
A heat pump, shown in Figure P22.26, is essentially an air conditioner installed backward. It extracts energy from colder air outside and deposits it in a warmer room. Suppose that the ratio of the actual energy entering the room to the work done by the device’s motor is 10.0% of the theoretical
How much work does an ideal Carnot refrigerator require to remove 1.00 J of energy from helium at 4.00 K and reject this energy to a room-temperature (293-K) environment?
A refrigerator maintains a temperature of 0°C in the cold compartment with a room temperature of 25.0°C. It removes energy from the cold compartment at the rate of 8 000 kJ/h. (a) What minimum power is required to operate the refrigerator? (b) The refrigerator exhausts energy into the room at
If a 35.0%-efficient Carnot heat engine (Fig. 22.2) is run in reverse so as to form a refrigerator (Fig. 22.5), what would be this refrigerator’s coefficient of performance?
Two Carnot engines have the same efficiency. One engine runs in reverse as a heat pump, and the other runs in reverse as a refrigerator. The coefficient of performance of the heat pump is 1.50 times the coefficient of performance of the refrigerator. Find (a) The coefficient of performance of the
In a cylinder of an automobile engine, just after combustion, the gas is confined to a volume of 50.0 cm3 and has an initial pressure of 3.00 X 106 Pa. The piston moves outward to a final volume of 300 cm3, and the gas expands without energy loss by heat. (a) If y = 1.40 for the gas, what is the
A gasoline engine has a compression ratio of 6.00 and uses a gas for which y = 1.40. (a) What is the efficiency (b) What If? If the actual efficiency is 15.0%, what fraction of the fuel is wasted as a result of friction and energy losses by heat that could by avoided in a reversible engine? (Assume
A 1.60-L gasoline engine with a compression ratio of 6.20 has a useful power output of 102 hp. assuming the engine operates in an idealized Otto cycle; find the energy taken in and the energy exhausted each second. Assume the fuel–air mixture behaves like an ideal gas with y = 1.40.
The compression ratio of an Otto cycle, as shown in Figure 22.13, is VA/VB = 8.00. At the beginning A of the compression process, 500 cm3 of gas is at 100 kPa and 20.0°C. At the beginning of the adiabatic expansion the temperature is TC = 750°C. Model the working fluid as an ideal gas with Eint =
An ice tray contains 500 g of liquid water at 0°C. Calculate the change in entropy of the water as it freezes slowly and completely at 0°C.
At a pressure of 1 atm, liquid helium boils at 4.20 K. The latent heat of vaporization is 20.5 kJ/kg. Determine the entropy change (per kilogram) of the helium resulting from vaporization
Calculate the change in entropy of 250 g of water heated slowly from 20.0°C to 80.0°C. (Suggestion: Note that dQ = mc dT)
In making raspberry jelly, 900 g of raspberry juice is combined with 930 g of sugar. The mixture starts at room temperature, 23.0°C, and is slowly heated on a stove until it reaches 220°F. It is then poured into heated jars and allowed to cool. Assume that the juice has the same specific heat as
What change in entropy occurs when a 27.9-g ice cube at -12°C is transformed into steam at 115°C?
The temperature at the surface of the Sun is approximately 5 700 K, and the temperature at the surface of the Earth is approximately 290 K. What entropy change occurs when 1 000 J of energy is transferred by radiation from the Sun to the Earth?
A 1 500-kg car is moving at 20.0 m/s. The driver brakes to a stop. The brakes cool off to the temperature of the surrounding air, which is nearly constant at 20.0°C. What is the total entropy change?
A 1.00-kg iron horseshoe is taken from a forge at 900°C and dropped into 4.00 kg of water at 10.0°C. Assuming that no energy is lost by heat to the surroundings, determine the total entropy change of the horseshoe-plus-water system.
How fast are you personally making the entropy of the Universe increase right now? Compute an order-of-magnitude estimate, stating what quantities you take as data and the values you measure or estimate for them.
A rigid tank of small mass contains 40.0 g of argon, initially at 200°C and 100 kPa. The tank is placed into a reservoir at 0°C and allowed to cool to thermal equilibrium. (a) Calculate the volume of the tank. (b) Calculate the change in internal energy of the argon. (c) Calculate the energy
A 1.00-mol sample of H2 gas is contained in the left-hand side of the container shown in Figure P22.45, which has equal volumes left and right. The right-hand side is evacuated. When the valve is opened, the gas streams into the right-hand side. What is the final entropy change of the gas? Does
A 2.00-L container has a center partition that divides it into two equal parts, as shown in Figure P22.46. The left side contains H2 gas, and the right side contains O2 gas. Both gases are at room temperature and at atmospheric pressure. The partition is removed, and the gases are allowed to mix.
A 1.00-mol sample of an ideal monatomic gas, initially at a pressure of 1.00 atm and a volume of 0.025 0 m3, is heated to a final state with a pressure of 2.00 atm and a volume of 0.040 0 m3. Determine the change in entropy of the gas in this process.
A 1.00-mol sample of a diatomic ideal gas, initially having pressure P and volume V, expands so as to have pressure 2P and volume 2V. Determine the entropy change of the gas in the process.
If you toss two dice, what is the total number of ways in which you can obtain (a) a 12 and (b) a 7?
Prepare a table like Table 22.1 for the following occurrence. You toss four coins into the air simultaneously and then record the results of your tosses in terms of the numbers of heads and tails that result. For example, HHTH and HTHH are two possible ways in which three heads and one tail can be
Repeat the procedure used to construct Table 22.1 (a) For the case in which you draw three marbles from your bag rather than four and (b) For the case in which you draw five rather than four.
Every second at Niagara Falls (Fig P22.52), some 5 000 m3 of water falls a distance of 50.0 m. What is the increase in entropy per second due to the falling water? Assume that the mass of the surroundings is so great that its temperature and that of the water stay nearly constant at 20.0°C.
A house loses energy through the exterior walls and roof at a rate of 5 000 J/s = 5.00 kW when the interior temperature is 22.0°C and the outside temperature is "5.00°C. Calculate the electric power required to maintain the interior temperature at 22.0°C for the following two cases. (a) The
How much work is required, using an ideal Carnot refrigerator, to change 0.500 kg of tap water at 10.0°C into ice at - 20.0°C? Assume the temperature of the freezer compartment is held at -20.0°C and the refrigerator exhausts energy into a room at 20.0°C.
A heat engine operates between two reservoirs at T2 = 600 K and T1 = 350 K. It takes in 1 000 J of energy from the higher-temperature reservoir and performs 250 J of work. Find (a) The entropy change of the Universe ΔSU for this process and (b) The work W that could have been done by an
Two identically constructed objects, surrounded by thermal insulation, are used as energy reservoirs for a Carnot engine. The finite reservoirs both have mass m and specific heat c. They start out at temperatures Th and Tc, where Th > Tc, (a) Show that the engine will stop working when the final
In 1816 Robert Stirling, a Scottish clergyman, patented the Stirling engine, which has found a wide variety of applications ever since. Fuel is burned externally to warm one of the engine’s two cylinders. A fixed quantity of inert gas moves cyclically between the cylinders, expanding in the hot
An electric power plant has an overall efficiency of 15.0%. The plant is to deliver 150 MW of power to a city, and its turbines use coal as the fuel. The burning coal produces steam that drives the turbines. This steam is then condensed to water at 25.0°C by passing it through cooling coils in
A power plant, having a Carnot efficiency, produces 1 000 MW of electrical power from turbines that take in steam at 500 K and reject water at 300 K into a flowing river. The water downstream is 6.00 K warmer due to the output of the power plant. Determine the flow rate of the river.
A power plant, having a Carnot efficiency, produces electric power from turbines that take in energy from steam at temperature Th and discharge energy at temperature Tc through a heat exchanger into a flowing river. The water downstream is warmer by ΔT due to the output of the power plant.
An athlete whose mass is 70.0 kg drinks 16 oz (453.6 g) of refrigerated water. The water is at a temperature of 35.0°F. (a) Ignoring the temperature change of the body that results from the water intake (so that the body is regarded as a reservoir always at 98.6°F), find the entropy increase of
A 1.00-mol sample of an ideal monatomic gas is taken through the cycle shown in Figure P22.62. The process A → B is a reversible isothermal expansion. Calculate (a) the net work done by the gas, (b) the energy added to the gas by heat, (c) the energy exhausted from the gas by heat, and (d)
A biology laboratory is maintained at a constant temperature of 7.00°C by an air conditioner, which is vented to the air outside. On a typical hot summer day the outside temperature is 27.0°C and the air conditioning unit emits energy to the outside at a rate of 10.0 kW. Model the unit as having
A 1.00-mol sample of an ideal gas expands isothermally, doubling in volume. (a) Show that the work it does in ex- panding is W = RT ln 2. (b) Because the internal energy Eint of an ideal gas depends solely on its temperature, the change in internal energy is zero during the expansion. It
A 1.00-mol sample of a monatomic ideal gas is taken through the cycle shown in Figure P22.65. At point A, the pressure, volume, and temperature are Pi , Vi , and Ti , respectively. In terms of R and Ti , find (a) the total energy entering the system by heat per cycle, (b) the total energy leaving
A sample consisting of n mol of an ideal gas undergoes a reversible isobaric expansion from volume Vi to volume 3Vi. Find the change in entropy of the gas by calculating
A system consisting of n mol of an ideal gas undergoes two reversible processes. It starts with pressure Pi and volume Vi, expands isothermally, and then contracts adiabatically to reach a final state with pressure Pi and volume 3Vi. (a) Find its change in entropy in the isothermal process. The
Suppose you are working in a patent office, and an inventor comes to you with the claim that her heat engine, which employs water as a working substance, has a thermodynamic efficiency of 0.61. She explains that it operates between energy reservoirs at 4°C and 0°C. It is a very complicated
An idealized diesel engine operates in a cycle known as the air-standard diesel cycle, shown in Figure 22.14. Fuel is sprayed into the cylinder at the point of maximum compression; B. Combustion occurs during the expansion B → C, which is modeled as an isobaric process. Show that the
A 1.00-mol sample of an ideal gas (y = 1.40) is carried through the Carnot cycle described in Figure 22.11. At point A, the pressure is 25.0 atm and the temperature is 600 K. At point C, the pressure is 1.00 atm and the temperature is 400 K. (a) Determine the pressures and volumes at points A, B,
Suppose 1.00 kg of water at 10.0°C is mixed with 1.00 kg of water at 30.0°C at constant pressure. When the mixture has reached equilibrium, (a) What is the final temperature? (b) Take cP = 4.19 kJ/kg K for water and show that the entropy of the system increases by
What are some factors that affect the efficiency of automobile engines?
In practical heat engines, which are we better able to control: the temperature of the hot reservoir or the temperature of the cold reservoir? Explain.
A steam-driven turbine is one major component of an electric power plant. Why is it advantageous to have the temperature of the steam as high as possible?
Is it possible to construct a heat engine that creates no thermal pollution? What does this tell us about environmental considerations for an industrialized society?
Does the second law of thermodynamics contradict or correct the first law? Argue for your answer.
“The first law of thermodynamics says you can’t really win, and the second law says you can’t even break even.” Explain how this statement applies to a particular device or process; alternatively, argue against the statement.
In solar ponds constructed in Israel, the Sun’s energy is concentrated near the bottom of a salty pond. With the proper layering of salt in the water, convection is prevented, and temperatures of 100°C may be reached. Can you estimate the maximum efficiency with which useful energy can be
Can a heat pump have a coefficient of performance less than unity? Explain.
Give various examples of irreversible processes that occur in nature. Give an example of a process in nature that is nearly reversible.
A heat pump is to be installed in a region where the average outdoor temperature in the winter months is - 20°C. In view of this, why would it be advisable to place the outdoor compressor unit deep in the ground? Why are heat pumps not commonly used for heating in cold climates?
The device shown in Figure Q22.11, called a thermoelectric converter, uses a series of semiconductor cells to convert internal energy to electric potential energy, which we will study in Chapter 25. In the photograph at the left, both legs of the device are at the same temperature, and no electric
Discuss three common examples of natural processes that involve an increase in entropy. Be sure to account for all parts of each system under consideration.
Discuss the change in entropy of a gas that expands (a) at constant temperature and (b) adiabatically.
A thermodynamic process occurs in which the entropy of a system changes by - 8.0 J/K. According to the second law of thermodynamics, what can you conclude about the entropy change of the environment?
If a supersaturated sugar solution is allowed to evaporate slowly, sugar crystals form in the container. Hence, sugar molecules go from a disordered form (in solution) to a highly ordered crystalline form. Does this process violate the second law of thermodynamics? Explain.
How could you increase the entropy of 1 mol of a metal that is at room temperature? How could you decrease its entropy?
Suppose your roommate is “Mr. Clean” and tidies up your messy room after a big party. Because your roommate is creating more order, does this represent a violation of the second law of thermodynamics?
Discuss the entropy changes that occur when you (a) Bake a loaf of bread and (b) Consume the bread.
“Energy is the mistress of the Universe and entropy is her shadow.” Writing for an audience of general readers, argue for this statement with examples. Alternatively, argue for the view that entropy is like a decisive hands-on executive instantly determining what will happen, while energy is
A classmate tells you that it is just as likely for all the air molecules in the room you are both in to be concentrated in one corner (with the rest of the room being a vacuum) as it is for the air molecules to be distributed uniformly about the room in their current state. Is this a true
If you shake a jar full of jellybeans of different sizes, the larger beans tend to appear near the top, and the smaller ones tend to fall to the bottom. Why? Does this process violate the second law of thermodynamics?
Use nodal analysis to find Io and I1 in the circuit shown below.Figure
A 20.0-L tank contains 0.225 kg of helium at I8.0°C. The molar mass of helium is 4.00 g/mol (a) How many moles of helium are in the tank? (b) What is the pressure in the tank, in Pascal and in atmospheres?
Helium gas with a volume of 2.60 L, under a pressure of 1.30 atm and at a temperature of 41.0oC, is warmed until both pressure and volume are doubled. (a) What is the final temperature? (b) How many grams of helium are there? The molar mass of helium is 4.00 g/mol
A cylindrical tank has a tight-fitting piston that allows the volume of the tank to be changed. The tank originally contains 0.110 m3 of air at a pressure of 3.40 atm. The piston is slowly pulled out until the volume of the gas is increased to 0.390 m3. If the temperature remains constant, what is
A 3.00-L tank contains air at 3.00 atm and 20.0oC. The tank is sealed and cooled until the pressure is 1.00 atm. (a) What is the temperature then in degrees Celsius? Assume that the volume of the tank is constant. (b) If the temperature is kept at the value found in part (a) and the gas is
(a) Use the ideal-gas law to estimate the number of air molecules in your physics lab room, assuming all the air is N2.(b) Calculate the particle density in the lab (that is, the number of molecules per cubic centimeter).
You have several identical balloons. You experimentally determine that a balloon will break if its volume exceeds 0.900 L. The pressure of the gas inside the balloon equals air pressure (1.00 atm. (a) If the air inside the balloon is at a constant temperature of 22.0oC and behaves as an ideal gas,
A Jaguar XK8 convertible has an eight-cylinder engine. At the beginning of its compression stroke, one of the cylinders contains 499 cm3 of air at atmospheric pressure (1.01 X 105 Pa) and a temperature of 27.0oC. At the end of the stroke, the air has been compressed to a volume of 46.2 cm3 and the
A welder using a tank of volume 0.0750 m' fills it with oxygen (molar mass 32.0 g/mol) at a gauge pressure of 3.00 X 105 Pa and temperature of 37.0°C. The tank has a small leak, and in time some of the oxygen leaks out. On a day when the temperature is 22.0°C, the gauge pressure of the oxygen in
A large cylindrical tank contains 0.750 m3 of nitrogen gas at 27°C and 1.50 X 105 Pa (absolute pressure). The tank has a tight fitting piston that allows the volume to be changed. What will be the pressure if the volume is decreased to 0.480 m3 and the temperature is increased to 157°C?
An empty cylindrical canister 1.50 m long and 90.0 cm in diameter is to be filled with pure oxygen at 22.0°C to store in a space station. To hold as much gas as possible, the absolute pressure of the oxygen will be 21.0 atm. The molar mass of oxygen is 32.0 g/mol (a) How many moles of oxygen does
The gas inside a balloon will always have a pressure nearly equal to atmospheric pressure, since that is the pressure applied to the outside of the balloon. You fill a balloon with helium (a nearly ideal gas) to a volume of 0.600 L at a temperature of 19.0°C. WhatIs the volume of the balloon if
Deviations from the Ideal-Gas Equation For carbon dioxide gas (CO2), the constants in the van der Waals equation are a = 0.364 j· m3/mol2 and b = 4.27 X 10-5 m3/mol (a) If 1.00 mol of CO2 gas at 350 K is confined to a volume of 400 cm3, find the pressure of the gas using the ideal-gas equation and
The total lung volume for a typical physics student is 6.00 L. A physics student fills her lungs with air at an absolute pressure of 1.00 atm. Then, holding her breath, she compresses her chest cavity, decreasing her lung volume to 5.70 L. What is the pressure of the air in her lungs then? Assume
A diver observes a bubble of air rising from the bottom of a lake (where the absolute pressure is 3.50 atm) to the surface (where the pressure is 1.00 atm). The temperature at the bottom is 4.0oC, and the temperature at the surface is 23.0oC. (a) What is the ratio of the volume of the bubble as it
A metal tank with volume 3.10 L will burst if the absolute pressure of the gas it contains exceeds 100 atm. (a) If 11.0 mol of an ideal gas is put into the tank at a temperature of 23.0oC, to what temperature can the gas be warmed before the tank ruptures? You can ignore the thermal expansion of
Three moles of an ideal gas are in a rigid cubical box with sides of length 0.200 m. (a) What is the force that the gas exerts on each of the six sides of the box when the gas temperature is 20.0oC? (b) What is the force when the temperature of the gas is increased to l00.0oC?
With the assumptions of Example 18.4 (Section 18.1), at what altitude above sea level is air pressure 90% of the pressure at sea level?

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Fundamentals of Physics 8th Extended edition Jearl Walker, Halliday Resnick - Solutions

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