Skip to main content

Bartleby Sitemap - Textbook Solutions

All Textbook Solutions for Principles of Physics: A Calculus-Based Text

A common material for cushioning objects in packages is made by trapping bubbles of air between sheets of plastic. Is this material more effective at keeping the contents of the package from moving around inside the package on (a) a hot day, (b) a cold day, or (c) either hot or cold days?16.4QQ Two containers hold an ideal gas at the same temperature and pressure. Both containers hold the same type of gas, but container B has twice the volume of container A. (i) What is the average translational kinetic energy per molecule in container B? (a) twice that of container A (b) the same as that of container A (c) half that of container A (d) impossible to determine (ii) From the same choices, describe the internal energy of the gas in container B.16.6QQ 1OQ A cylinder with a piston holds 0.50 m3 of oxygen at an absolute pressure of 4.0 atm. The piston is pulled outward, increasing the volume of the gas until the pressure drops to 1.0 atm. If the temperature stays constant, what new volume does the gas occupy? (a) 1.0 m3 (b) 1.5 m3 (c) 2.0 m3 (d) 0.12 m3 (e) 2.5 m3 A hole is drilled in a metal plate. When the metal is raised to a higher temperature, what happens to the diameter of the hole? (a) It decreases. (b) It increases. (c) It remains the same. (d) The answer depends on the initial temperature of the metal. (e) None of those answers is correct.When a certain gas under a pressure of 5.00 106 Pa at 25.0C is allowed to expand to 3.00 times its original volume, its final pressure is 1.07 106 Pa. What is its final temperature? (a) 450 K (b) 233 K (c) 212 K (d) 191 K (e) 115 K 5OQ 6OQ What would happen if the glass of a thermometer expanded more on warming than did the liquid in the tube? (a) The thermometer would break. (b) It could be used only for temperatures below room temperature. (c) You would have to hold it with the bulb on top. (d) The scale on the thermometer is reversed so that higher temperature values would be found closer to the bulb. (e) The numbers would not be evenly spaced.8OQ A gas is at 200 K. If we wish to double the rms speed of the molecules of the gas, to what value must we raise its temperature? (a) 283 K (b) 400 K (c) 566 K (d) 800 K (e) 1 130 K 10OQ 11OQ A rubber balloon is filled with 1 L of air at 1 atm and 300 K and is then put into a cryogenic refrigerator at 100 K. The rubber remains flexible as it cools. (i) What happens to the volume of the balloon? (a) It decreases to 13L. (b) It decreases to 1/3L. (c) It is constant. (d) It increases to 3L. (e) It increases to 3 L. (ii) What happens to the pressure of the air in the balloon? (a) It decreases to 13atm. (b) It decreases to 1/3atm. (c) It is constant. (d) It increases to 3atm. (e) It increases to 3 atm.13OQ An ideal gas is contained in a vessel at 300 K. The temperature of the gas is then increased to 900 K. (i) By what factor does the average kinetic energy of the molecules change, (a) a factor of 9, (b) a factor of 3, (c) a factor of 3, (d) a factor of 1, or (e) a factor of 13? Using the same choices as in part (i), by what factor does each of the following change: (ii) the rms molecular speed of the molecules, (iii) the average momentum change that one molecule undergoes in a collision with one particular wall, (iv) the rate of collisions of molecules with walls, and (v) the pressure of the gas?15OQ 16OQ 17OQ A sample of gas with a thermometer immersed in the gas is held over a hot plate. A student is asked to give a step-by-step account of what makes our observation of the temperature of the gas increase. His response includes the following steps. (a) The molecules speed up. (b) Then the molecules collide with one another more often. (c) Internal friction makes the collisions inelastic. (d) Heat is produced in the collisions. (e) The molecules of the gas transfer more energy to the thermometer when they strike it, so we observe that the temperature has gone up. (f) The same process can take place without the use of a hot plate if you quickly push in the piston in an insulated cylinder containing the gas. (i) Which of the parts (a) through (f) of this account are correct statements necessary for a clear and complete explanation? (ii) Which are correct statements that are not necessary to account for the higher thermometer reading? (iii) Which are incorrect statements?19OQ 1CQ 2CQ 3CQ A piece of copper is dropped into a beaker of water. (a) If the waters temperature rises, what happens to the temperature of the copper? (b) Under what conditions are the water and copper in thermal equilibrium?5CQ 6CQ 7CQ 8CQ 9CQ 10CQ 11CQ 12CQ 13CQ 1P Convert the following to equivalent temperatures on the Celsius and Kelvin scales: (a) the normal human body temperature, 98.6F; (b) the air temperature on a cold day, 5.00F.3P 4P 5P 6P 7P 8P 9P A sample of a solid substance has a mass m and a density 0 at a temperature T0. (a) Find the density of the substance if its temperature is increased by an amount T in terms of the coefficient of volume expansion b. (b) What is the mass of the sample if the temperature is raised by an amount T?Each year thousands of children are badly burned by hot tap water. Figure P16.11 shows a cross-sectional view of an antiscalding faucet attachment designed to prevent such accidents. Within the device, a spring made of material with a high coefficient of thermal expansion controls a movable plunger. When the water temperature rises above a preset safe value, the expansion of the spring causes the plunger to shut off the water flow. Assuming that the initial length L of the unstressed spring is 2.40 cm and its coefficient of linear expansion is 22.0 106 (C)1, determine the increase in length of the spring when the water temperature rises by 30.0C. (You will find the increase in length to be small. Therefore, to provide a greater variation in valve opening for the temperature change anticipated, actual devices have a more complicated mechanical design.)12P 13P 14P The active element of a certain laser is made of a glass rod 30.0 cm long and 1.50 cm in diameter. Assume the average coefficient of linear expansion of the glass is equal to 9.00 106 (C)1. If the temperature of the rod increases by 65.0C, what is the increase in (a) its length, (b) its diameter, and (c) its volume?16P 17P 18P 19P 20P 21P 22P 23P 24P 25P 26P 27P 28P The mass of a hot-air balloon and its cargo (not including the air inside) is 200 kg. The air outside is at 10.0C and 101 kPa. The volume of the balloon is 400 m3. To what temperature must the air in the balloon be warmed before the balloon will lift off? (Air density at 10.0C is 1.244 kg/m3.)30P A popular brand of cola contains 6.50 g of carbon dioxide dissolved in 1.00 L of soft drink. If the evaporating carbon dioxide is trapped in a cylinder at 1.00 atm and 20.0C, what volume does the gas occupy?32P At 25.0 m below the surface of the sea, where the temperature is 5.00C, a diver exhales an air bubble having a volume of 1.00 cm3. If the surface temperature of the sea is 20.0C, what is the volume of the bubble just before it breaks the surface?To measure how far below the ocean surface a bird dives to catch a fish, a scientist uses a method originated by Lord Kelvin. He dusts the interiors of plastic tubes with powdered sugar and then seals one end of each tube. He captures the bird at nighttime in its nest and attaches a tube to its back. He then catches the same bird the next night and removes the tube. In one trial, using a tube 6.50 cm long, water washes away the sugar over a distance of 2.70 cm from the open end of the tube. Find the greatest depth to which the bird dived, assuming the air in the tube stayed at constant temperature.35P 36P 37P 38P 39P A cylinder contains a mixture of helium and argon gas in equilibrium at 150C. (a) What is the average kinetic energy for each type of gas molecule? (b) What is the rms speed of each type of molecule?41P 42P 43P (a) How many atoms of helium gas fill a spherical balloon of diameter 30.0 cm at 20.0C and 1.00 atm? (b) What is the average kinetic energy of the helium atoms? (c) What is the rms speed of the helium atoms?Fifteen identical particles have various speeds: one has a speed of 2.00 m/s, two have speeds of 3.00 m/s, three have speeds of 5.00 m/s, four have speeds of 7.00 m/s, three have speeds of 9.00 m/s, and two have speeds of 12.0 m/s. Find (a) the average speed, (b) the rms speed, and (c) the most probable speed of these particles.From the MaxwellBoltzmann speed distribution, show that the most probable speed of a gas molecule is given by Equation 16.23. Note: The most probable speed corresponds to the point at which the slope of the speed distribution curve dNv/dv is zero.47P Helium gas is in thermal equilibrium with liquid helium at 4.20 K. Even though it is on the point of condensation, model the gas as ideal and determine the most probable speed of a helium atom (mass = 6.64 1027 kg) in it.49P 50P 51P 52P A mercury thermometer is constructed as shown in Figure P16.53. The Pyrex glass capillary tube has a diameter of 0.004 00 cm, and the bulb has a diameter of 0.250 cm. Find the change in height of the mercury column that occurs with a temperature change of 30.0C.A liquid with a coefficient of volume expansion just fills a spherical shell of volume V (Fig. P16.53). The shell and the open capillary of area A projecting from the top of the sphere are made of a material with an average coefficient of linear expansion . The liquid is free to expand into the capillary. Assuming the temperature increases by T, find the distance h the liquid rises in the capillary.A clock with a brass pendulum has a period of 1.000 s at 20.0C. If the temperature increases to 30.0C, (a) by how much does the period change and (b) how much time does the clock gain or lose in one week?A vertical cylinder of cross-sectional area A is fitted with a tight-fitting, frictionless piston of mass m (Fig. P16.56). The piston is not restricted in its motion in any way and is supported by the gas at pressure P below it. Atmospheric pressure is P0. We wish to find die height h in Figure P16.56. (a) What analysis model is appropriate to describe the piston? (b) Write an appropriate force equation for the piston from this analysis model in terms of P, P0, m, A, and g. (c) Suppose n moles of an ideal gas are in the cylinder at a temperature of T. Substitute for P in your answer to part (b) to find the height h of the piston above the bottom of the cylinder.57P 58P 59P The rectangular plate shown in Figure P16.60 has an area Ai equal to w. If the temperature increases by T, each dimension increases according to Equation 16.4, where is the average coefficient of linear expansion. (a) Show that the increase in area is A = 2Ai T. (b) What approximation does this expression assume?In a chemical processing plant, a reaction chamber of fixed volume V0 is connected to a reservoir chamber of fixed volume 4V0 by a passage containing a thermally insulating porous plug. The plug permits the chambers to be at different temperatures. The plug allows gas to pass from either chamber to the other, ensuring that the pressure is the same in both. At one point in the processing, both chambers contain gas at a pressure of 1.00 atm and a temperature of 27.0C. Intake and exhaust valves to the pair of chambers are closed. The reservoir is maintained at 27.0C while the reaction chamber is heated to 400C. What is the pressure in both chambers after that is done?62P 63P Two concrete spans that form a bridge of length L are placed end to end so that no room is allowed for expansion (Fig. P16.63a). If a temperature increase of T occurs, what is the height y to which the spans rise when they buckle (Fig. P16.63b)?A 1.00-km steel railroad rail is fastened securely at both ends when the temperature is 20.0C. As the temperature increases, the rail buckles, taking the shape of an arc of a vertical circle. Find the height h of the center of the rail when the temperature is 25.0C. (You will need to solve a transcendental equation.)66P 67P 68P Consider an object with any one of the shapes displayed in Table 10.2. What is the percentage increase in the moment of inertia of the object when it is warmed from 0C to 100C if it is composed of (a) copper or (b) aluminum? Assume the average linear expansion coefficients shown in Table 16.1 do not vary between 0C and 100C. (c) Why are the answers for parts (a) and (b) the same for all the shapes?70P 71P 72P 73P A cylinder that has a 40.0-cm radius and is 50.0 cm deep is filled with air at 20.0C and 1.00 atm (Fig. P10.74a). A 20.0-kg piston is now lowered into the cylinder, compressing the air trapped inside as it takes equilibrium height hi (Fig. P16.74b). Finally, a 25.0-kg dog stands on the piston, further compressing the air, which remains at 20C (Fig. P16.74c). (a) How far down (h) does the piston move when the dog steps onto it? (b) To what temperature should the gas be warmed to raise the piston and dog back to hi?75P 17.1QQ 17.2QQ 17.3QQ 17.4QQ Characterize the paths in Figure 17.10 as isobaric, isovolumetric, isothermal, or adiabatic. For path B, Q = 0. The blue curves are isotherms. Figure 17.10 (Quick Quiz 17.5) Identify the nature of paths A, B, C, and D.(i) How does the internal energy of an ideal gas change as it follows path i f in Active Figure 17.13? (a) Eint increases. (b) Eint decreases. (c) Eint stays the same. (d) There is not enough information to determine how Eint changes. (ii) From the same choices, how does the internal energy of a gas change as it follows path f f along the isotherm labeled T + T in Active Figure 17.13?17.7QQ 1OQ A 100-g piece of copper, initially at 95.0C, is dropped into 200 g of water contained in a 280-g aluminum can; the water and can are initially at 15.0C. What is the final temperature of the system? (Specific heats of copper and aluminum are 0.092 and 0.215 cal/g C, respectively.) (a) 16C (b) 18C (c) 24C (d) 26C (e) none of those answers 3OQ 4OQ 5OQ 6OQ 7OQ 8OQ 9OQ 10OQ Star A has twice the radius and twice the absolute surface temperature of star B. The emissivity of both stars can be assumed to be 1. What is the ratio of the power output of star A to that of star B? (a) 4 (b) 8 (c) 16 (d) 32 (e) 64 If a gas is compressed isothermally, which of the following statements is true? (a) Energy is transferred into the gas by heat. (b) No work is done on the gas. (c) The temperature of the gas increases. (d) The internal energy of the gas remains constant. (e) None of those statements is true.When a gas undergoes an adiabatic expansion, which of the following statements is true? (a) The temperature of the gas does not change. (b) No work is done by the gas. (c) No energy is transferred to the gas by heat. (d) The internal energy of the gas does not change. (e) The pressure increases.Ethyl alcohol has about one-half the specific heat of water. Assume equal amounts of energy are transferred by heat into equal-mass liquid samples of alcohol and water in separate insulated containers. The water rises in temperature by 25C. How much will the alcohol rise in temperature? (a) It will rise by 12C. (b) It will rise by 25C. (c) It will rise by 50C. (d) It depends on the rate of energy transfer. (e) It will not rise in temperature.15OQ 1CQ 2CQ Pioneers stored fruits and vegetables in underground cellars. In winter, why did the pioneers place an open barrel of water alongside their produce?Why is a person able to remove a piece of dry aluminum foil from a hot oven with bare fingers, whereas a burn results if there is moisture on the foil?5CQ 6CQ It is the morning of a day that will become hot. You just purchased drinks for a picnic and are loading them, with ice, into a chest in the back of your car. (a) You wrap a wool blanket around the chest. Does doing so help to keep the beverages cool, or should you expect the wool blanket to warm them up? Explain your answer. (b) Your younger sister suggests you wrap her up in another wool blanket to keep her cool on the hot day like the ice chest. Explain your response to her.You need to pick up a very hot cooking pot in your kitchen. You have a pair of cotton oven mitts. To pick up the pot most comfortably, should you soak them in cold water or keep them dry?Rub the palm of your hand on a metal surface for about 30 seconds. Place the palm of your other hand on an un-rubbed portion of the surface and then on the rubbed portion. The rubbed portion will feel warmer. Now repeat this process on a wood surface. Why does the temperature difference between the rubbed and unrubbed portions of the wood surface seem larger than for the metal surface?10CQ 11CQ 12CQ On his honeymoon, James Joule traveled from England to Switzerland. He attempted to verify his idea of the inter-convertibility of mechanical energy and internal energy by measuring the increase in temperature of water that fell in a waterfall. For the waterfall near Chamonix in the French Alps, which has a 120-m drop, what maximum temperature rise could Joule expect? He did not succeed in measuring it, partly because evaporation cooled the falling water and also because his thermometer was not sufficiently sensitive.Consider Joules apparatus described in Figure P17.2. The mass of each of the two blocks is 1.50 kg, and the insulated tank is filled with 200 g of water. What is the increase in the waters temperature after the blocks fall through a distance of 3.00 m? Figure P17.2.3P 4P 5P 6P 7P 8P 9P 10P 11P 12P 13P 14P In an insulated vessel, 250 g of ice at 0C is added to 600 g of water at 18.0C. (a) What is the final temperature of the system? (b) How much ice remains when the system reaches equilibrium?16P 17P 18P A 1.00-kg block of copper at 20.0C is dropped into a large vessel of liquid nitrogen at 77.3 K. How many kilograms of nitrogen boil away by the time the copper reaches 77.3 K? (The specific heat of copper is 0.092 4 cal/g C, and the latent heat of vaporization of nitrogen is 48.0 cal/g.)A resting adult of average size converts chemical energy in food into internal energy at the rate 120 W, called her basal metabolic rate. To stay at constant temperature, the body must put out energy at the same rate. Several processes exhaust energy from your body. Usually, the most important is thermal conduction into the air in contact with your exposed skin. If you are not wearing a hat, a convection current of warm air rises vertically from your head like a plume from a smokestack. Your body also loses energy by electromagnetic radiation, by your exhaling warm air, and by evaporation of perspiration. In this problem, consider still another pathway for energy loss: moisture in exhaled breath. Suppose you breathe out 22.0 breaths per minute, each with a volume of 0.600 L. Assume that you inhale dry air and exhale air at 37C containing water vapor with a vapor pressure of 3.20 kPa. The vapor came from evaporation of liquid water in your body. Model the water vapor as an ideal gas. Assume that its latent heat of evaporation at 37C is the same as its heat of vaporization at 100C. Calculate the rate at which you lose energy by exhaling humid air.21P 22P An ideal gas is enclosed in a cylinder with a movable piston on top of it. The piston has a mass of 8 000 g and an area of 5.00 cm2 and is free to slide up and down, keeping the pressure of the gas constant. How much work is done on the gas as the temperature of 0.200 mol of the gas is raised from 20.0C to 300C?24P 25P A sample of an ideal gas goes through the process shown in Figure P17.26. From A to B, the process is adiabatic; from B to C, it is isobaric with 100 kJ of energy entering the system by heat; from C to D, the process is isothermal; and from D to A, it is isobaric with 150 kJ of energy leaving the system by heat. Determine the difference in internal energy Eint,B Eint,A.A thermodynamic system undergoes a process in which its internal energy decreases by 500 J. Over the same time interval, 220 J of work is done on the system. Find the energy transferred from it by heat.A gas is taken through the cyclic process described in Figure P17.28. (a) Find the net energy transferred to the system by heat during one complete cycle. (b) What If? If the cycle is reversedthat is, the process follows the path ACBAwhat is the net energy input per cycle by heat?Consider the cyclic process depicted in Figure P17.28. If Q is negative for the process BC and Eint is negative for the process CA, what are the signs of Q, W, and Eint that are associated with each of the three processes?Why is the following situation impossible? An ideal gas undergoes a process with the following parameters: Q = 10.0 J, W = 12.0 J, and T = 2.00C.An ideal gas initially at 300 K undergoes an isobaric expansion at 2.50 kPa. If the volume increases from 1.00 m3 to 3.00 m3 and 12.5 kJ is transferred to the gas by heat, what are (a) the change in its internal energy and (b) its final temperature?In Figure P17.32, the change in internal energy of a gas that is taken from A to C along the blue path is +800 J. The work done on the gas along the red path ABC is 500 J. (a) How much energy must be added to the system by heat as it goes from A through B to C? (b) If the pressure at point A is five times that of point C, what is the work done on the system in going from C to D? (c) What is the energy exchanged with the surroundings by heat as the gas goes from C to A along the green path? (d) If the change in internal energy in going from point D to point A is +500 J, how much energy must be added to the system by heat as it goes from point C to point D? Figure P17.32 33P 34P 35P 36P 37P One mole of an ideal gas does 3 000 J of work on its surroundings as it expands isothermally to a final pressure of 1.00 atm and volume of 25.0 L. Determine (a) the initial volume and (b) the temperature of the gas.A 1.00-mol sample of hydrogen gas is heated at constant pressure from 300 K to 420 K. Calculate (a) the energy transferred to the gas by heat, (b) the increase in its internal energy, and (c) the work done on the gas.A sample of a diatomic ideal gas has pressure P and volume V. When the gas is warmed, its pressure triples and its volume doubles. This warming process includes two steps, the first at constant pressure and the second at constant volume. Determine the amount of energy transferred to the gas by heat.41P 42P 43P Review. This problem is a continuation of Problem 16.29 in Chapter 16. A hot-air balloon consists of an envelope of constant volume 400 m3. Not including the air inside, the balloon and cargo have mass 200 kg. The air outside and originally inside is a diatomic ideal gas at 10.0C and 101 kPa, with density 1.25 kg/m3. A propane burner at the center of the spherical envelope injects energy into the air inside. The air inside stays at constant pressure. Hot air, at just the temperature required to make the balloon lift off, starts to fill the envelope at its closed top, rapidly enough so that negligible energy flows by heat to the cool air below it or out through the wall of the balloon. Air at 10C leaves through an opening at the bottom of the envelope until the whole balloon is filled with hot air at uniform temperature. Then the burner is shut off and the balloon rises from the ground. (a) Evaluate the quantity of energy the burner must transfer to the air in the balloon. (b) The heat value of propanethe internal energy released by burning each kilogramis 50.3 MJ/kg. What mass of propane must be burned?45P A 2.00-mol sample of a diatomic ideal gas expands slowly and adiabatically from a pressure of 5.00 atm and a volume of 12.0 L to a final volume of 30.0 L. (a) What is the final pressure of the gas? (b) What are the initial and final temperatures? Find (c) Q, (d) Eint, and (e) W for the gas during this process.47P An ideal gas with specific heat ratio confined to a cylinder is put through a closed cycle. Initially, the gas is at Pi, Vi, and Ti. First, its pressure is tripled under constant volume. It then expands adiabatically to its original pressure and finally is compressed isobarically to its original volume. (a) Draw a PV diagram of this cycle. (b) Determine the volume at the end of the adiabatic expansion. Find (c) the temperature of the gas at the start of the adiabatic expansion and (d) the temperature at the end of the cycle. (e) What was the net work done on the gas for this cycle?49P 50P 51P 52P Air (a diatomic ideal gas) at 27.0C and atmospheric pressure is drawn into a bicycle pump (Figure P17.53) that has a cylinder with an inner diameter of 2.50 cm and length 50.0 cm. The downstroke adiabatically compresses the air, which reaches a gauge pressure of 8.00 105 Pa before entering the tire. We wish to investigate the temperature increase of the pump. (a) What is the initial volume of the air in the pump? (b) What is the number of moles of air in the pump? (c) What is the absolute pressure of the compressed air? (d) What is the volume of the compressed air? (e) What is the temperature of the compressed air? (f) What is the increase in internal energy of the gas during the compression? What If? The pump is made of steel that is 2.00 mm thick. Assume 4.00 cm of the cylinders length is allowed to come to thermal equilibrium with the air. (g) What is the volume of steel in this 4.00-cm length? (h) What is the mass of steel in this 4.00-cm length? (i) Assume the pump is compressed once. After the adiabatic expansion, conduction results in the energy increase in part (f) being shared between the gas and the 4.00-cm length of steel. What will be the increase in temperature of the steel after one compression? Figure P17.53 54P 55P 56P 57P 58P 59P 60P 61P 62P The surface of the Sun has a temperature of about 5 800 K. The radius of the Sun is 6.96 108 m. Calculate the total energy radiated by the Sun each second. Assume the emissivity of the Sun is 0.986.64P At high noon, the Sun delivers 1 000 W to each square meter of a blacktop road. If the hot asphalt transfers energy only by radiation, what is its steady-state temperature?A theoretical atmospheric lapse rate. Section 16.7 described experimental data on the decrease in temperature with altitude in the Earths atmosphere. Model the troposphere as an ideal gas, everywhere with equivalent molar mass M and ratio of specific heats y. Absorption of sunlight at the Earths surface warms the troposphere from below, so vertical convection currents are continually mixing the air. As a parcel of air rises, its pressure drops and it expands. The parcel does work on its surroundings, so its internal energy decreases and it drops in temperature. Assume that the vertical mixing is so rapid as to be adiabatic. (a) Show that the quantity TP (1 )/ has a uniform value through the layers of the troposphere. (b) By differentiating with respect to altitude y, show that the lapse rate is given by dTdy=TP(11)dPdy (c) A lower layer of air must support the weight of the layers above. From Equation 15.4, observe that mechanical equilibrium of the atmosphere requires that the pressure decrease with altitude according to dP/dy = g. The depth of the troposphere is small compared with the radius of the Earth, so you may assume that the free-fall acceleration is uniform. Proceed to prove that the lapse rate is dTdy=(11)MgR Problem 16.50 in Chapter 16 calls for evaluation of this theoretical lapse rate on the Earth and on Mars and for comparison with experimental results.67P A sample of a monatomic ideal gas occupies 5.00 L at atmospheric pressure and 300 K (point A in Fig. P17.68). It is warmed at constant volume to 3.00 atm (point B). Then it is allowed to expand isothermally to 1.00 atm (point C) and at last compressed isobarically to its original state. (a) Find the number of moles in the sample. Find (b) the temperature at point B, (c) the temperature at point C, and (d) the volume at point C. (e) Now consider the processes A B, B C, and C A. Describe how to carry out each process experimentally. (f) Find Q, W, and Eint for each of the processes. (g) For the whole cycle A B C A, find Q, W, and Eint. Figure P17.68 An aluminum rod 0.500 m in length and with a cross-sectional area of 2.50 cm2 is inserted into a thermally insulated vessel containing liquid helium at 4.20 K. The rod is initially at 300 K. (a) If one-half of the rod is inserted into the helium, how many liters of helium boil off by the time the inserted half cools to 4.20 K? Assume the upper half does not yet cool. (b) If the circular surface of the upper end of the rod is maintained at 300 K, what is the approximate boil-off rate of liquid helium in liters per second after the lower half has reached 4.20 K? (Aluminum has thermal conductivity of 3 100 W/m K at 4.20 K; ignore its temperature variation. The density of liquid helium is 125 kg/m3.)70P 71P 72P 73P 74P 75P 76P 77P 78P 79P 81P 82P 84P 85P 86P 87P 88P Water in an electric teakettle is boiling. The power absorbed by the water is 1.00 kW. Assuming the pressure of vapor in the kettle equals atmospheric pressure, determine the speed of effusion of vapor from the kettles spout if the spout has a cross-sectional area of 2.00 cm2. Model the steam as an ideal gas.The energy input to an engine is 3.00 times greater than the work it performs. (i) What is its thermal efficiency? (a) 3.00 (b) 1.00 (c) 0.333 (d) impossible to determine (ii) What fraction of the energy input is expelled to the cold reservoir? (a) 0.333 (b) 0.667 (c) 1.00 (d) impossible to determine 18.2QQ 18.3QQ (a) Suppose you select four cards at random from a standard deck of playing cards and end up with a macrostate of four deuces. How many microstates are associated with this macrostate? (b) Suppose you pick up two cards and end up with a macrostate of two aces. How many microstates are associated with this macrostate?Which of the following is true for the entropy change of a system that undergoes a reversible, adiabatic process? (a) S 0 (b) S = 0 (c) S 0 An ideal gas is taken from an initial temperature Ti to a higher final temperature Tf along two different reversible paths. Path A is at constant pressure, and path B is at constant volume. What is the relation between the entropy changes of the gas for these paths? (a) SA SB (b) SA = SB (c) SA SB True or False: The entropy change in an adiabatic process must be zero because Q = 0.1OQ 2OQ A refrigerator has 18.0 kJ of work done on it while 115 kJ of energy is transferred from inside its interior. What is its coefficient of performance? (a) 3.40 (b) 2.80 (c) 8.90 (d) 6.40 (e) 5.20 4OQ Consider cyclic processes completely characterized by each of the following net energy inputs and outputs. In each case, the energy transfers listed are the only ones occurring. Classify each process as (a) possible, (b) impossible according to the first law of thermodynamics, (c) impossible according to the second law of thermodynamics, or (d) impossible according to both the first and second laws. (i) Input is 5 J of work, and output is 4 J of work. (ii) Input is 5 J of work, and output is 5 J of energy transferred by heat. (iii) Input is 5 J of energy transferred by electrical transmission, and output is 6 J of work. (iv) Input is 5 J of energy transferred by heat, and output is 5 J of energy transferred by heat. (v) Input is 5 J of energy transferred by heat, and output is 5 J of work. (vi) Input is 5 J of energy transferred by heat, and output is 3 J of work plus 2 J of energy transferred by heat.6OQ 7OQ 8OQ A sample of a monatomic ideal gas is contained in a cylinder with a piston. Its state is represented by the dot in the PV diagram shown in Figure OQ18.9. Arrows A through E represent isobaric, isothermal, adiabatic, and isovolumetric processes that the sample can undergo. In each process except D, the volume changes by a factor of 2. All five processes are reversible. Rank the processes according to the change in entropy of the gas from the largest positive value to the largest-magnitude negative value. In your rankings, display any cases of equality. Figure OQ18.9 Assume a sample of an ideal gas is at room temperature. What action will necessarily make the entropy of the sample increase? (a) Transfer energy into it by heat. (b) Transfer energy into it irreversibly by heat. (c) Do work on it. (d) Increase either its temperature or its volume, without letting the other variable decrease. (e) None of those choices is correct.11OQ 1CQ 2CQ 3CQ 4CQ 5CQ 6CQ 7CQ 8CQ 9CQ 10CQ 11CQ Discuss three different common examples of natural processes that involve an increase in entropy. Be sure to account for all parts of each system under consideration.The energy exhaust from a certain coal-fired electric generating station is carried by cooling water into Lake Ontario. The water is warm from the viewpoint of living things in the lake. Some of them congregate around the outlet port and can impede the water flow. (a) Use the theory of heat engines to explain why this action can reduce the electric power output of the station. (b) An engineer says that the electric output is reduced because of higher back pressure on the turbine blades. Comment on the accuracy of this statement.1P 2P 3P 4P 5P 6P 7P 8P 9P 10P 11P 12P 13P 14P Argon enters a turbine at a rate of 80.0 kg/min, a temperature of 800C, 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. (c) The turbine is one component of a model closed-cycle gas turbine engine. Calculate the maximum efficiency of the engine.16P A refrigerator has a coefficient of performance equal to 5.00. The refrigerator takes in 120 J of energy from a cold reservoir in each cycle. Find (a) the work required in each cycle and (b) the energy expelled to the hot reservoir.18P 19P In 1993, the U.S. government instituted a requirement that all room air conditioners sold in the United States must have an energy efficiency ratio (EER) of 10 or higher. The EER is defined as the ratio of the cooling capacity of the air conditioner, measured in British thermal units per hour, or Btu/h, to its electrical power requirement in watts. (a) Convert the EER of 10.0 to dimensionless form, using the conversion 1 Btu = 1 055 J. (b) What is the appropriate name for this dimensionless quantity? (c) In the 1970s, it was common to find room air conditioners with EERs of 5 or lower. State how the operating costs compare for 10 000-Btu/h air conditioners with EERs of 5.00 and 10.0. Assume each air conditioner operates for 1 500 h during the summer in a city where electricity costs 17.0 per kWh.21P 22P 23P 24P A heat pump used for heating shown in Figure P18.25 is essentially an air conditioner installed backward. It extracts energy from colder air outside and deposits it in a warmer room. Suppose the ratio of the actual energy entering the room to the work done by the devices motor is 10.0% of the theoretical maximum ratio. Determine the energy entering the room per joule of work done by the motor given that the inside temperature is 20.0C and the outside temperature is 5.00C. Figure P18.25 26P 27P An ice tray contains 500 g of liquid water at 0C. Calculate the change in entropy of the water as it freezes slowly and completely at 0C.29P 30P 31P (a) Prepare a table like Table 18.1 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 (H) and tails (T) that result. For example, HHTH and HTHH are two possible ways in which three heads and one tail can be achieved. (b) On the basis of your table, what is the most probable result recorded for a toss? In terms of entropy, (c) what is the most ordered macrostate, and (d) what is the most disordered?33P 34P 35P 36P 37P

Page: [1][2][3][4][5][6][7][8][9][10][11]