?Figure 18-27 shows two closed cycles on p-V diagrams for a gas. The three parts of

The initial length L, change in temperature \(\Delta T\), and change in length \(\Delta L\) of four rods are given in the following table. Rank the rods according to their coefficients of thermal expansion, greatest first. Text Transcription: Delta T Delta L

Figure 18-24 shows three linear temperature scales, with the freezing and boiling points of water indicated. Rank the three scales according to the size of one degree on them, greatest first.

Question 4 continued: Graphs b through f of Fig. 18-25 are additional sketches of T versus t, of which one or more are impossible to produce. (a) Which is impossible and why? (b) In the possible ones, is the equilibrium temperature above, below, or at the freezing point of water? (c) As the possible situations reach equilibrium, does the liquid partly freeze, fully freeze, or undergo no freezing? Does the ice partly melt, fully melt, or undergo no melting?

Figure 18-26 shows three different arrangements of materials 1, 2, and 3 to form a wall. The thermal conductivities are \(k_{1}>k_{2}>k_{3}\). The left side of the wall is \(20 \mathrm{C}^{\circ}\) higher than the right side. Rank the arrangements according to (a) the (steady state) rate of energy conduction through the wall and (b) the temperature difference across material 1, greatest first. Text Transcription: k_1>k_2>k_3 20C^circ

Figure 18-27 shows two closed cycles on p-V diagrams for a gas. The three parts of cycle 1 are of the same length and shape as those of cycle 2. For each cycle, should the cycle be traversed clockwise or counterclockwise if (a) the net work W done by the gas is to be positive and (b) the net energy transferred by the gas as heat Q is to be positive?

Three different materials of identical mass are placed one at a time in a special freezer that can extract energy from a material at a certain constant rate. During the cooling process, each material begins in the liquid state and ends in the solid state; Fig. 18-28 shows the temperature T versus time t. (a) For material 1, is the specific heat for the liquid state greater than or less than that for the solid state? Rank the materials according to (b) freezing-point temperature, (c) specific heat in the liquid state, (d) specific heat in the solid state, and (e) heat of fusion, all greatest first.

A hot object is dropped into a thermally insulated container of water, and the object and water are then allowed to come to thermal equilibrium. The experiment is repeated twice, with different hot objects. All three objects have the same mass and initial temperature, and the mass and initial temperature of the water are the same in the three experiments. For each of the experiments, Fig. 18?29 gives graphs of the temperatures T of the object and the water versus time t. Rank the graphs according to the specific heats of the objects, greatest first.

In the extrusion of cold chocolate from a tube, work is done on the chocolate by the pressure applied by a ram forcing the chocolate through the tube. The work per unit mass of extruded chocolate is equal to \(p / \rho\), where p is the difference between the applied pressure and the pressure where the chocolate emerges from the tube, and \(\rho\) is the density of the chocolate. Rather than increasing the temperature of the chocolate, this work melts cocoa fats in the chocolate. These fats have a heat of fusion of 150 kJ/kg. Assume that all of the work goes into that melting and that these fats make up 30% of the chocolate’s mass. What percentage of the fats melt during the extrusion if p = 5.5 MPa and \(\rho=1200 \mathrm{kg} / \mathrm{m}^{3}\)? Text Transcription: p/rho rho rho = 1200 kg/m^3

Figure 18-51 displays a closed cycle for a gas. The change in internal energy along path ca is ?160 J. The energy transferred to the gas as heat is 200 J along path ab, and 40 J along path bc. How much work is done by the gas along (a) path abc and (b) path ab?

In a certain solar house, energy from the Sun is stored in barrels filled with water. In a particular winter stretch of five cloudy days,\(1.00 \times 10^{6}\) kcal is needed to maintain the inside of the house at \(22.0^{\circ} \mathrm{C}\). Assuming that the water in the barrels is at \(50.0^{\circ} \mathrm{C}\) and that the water has a density of \(1.00 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3}\), what volume of water is required? Text Transcription: 1.00 times 10^6 22.0^circ C 50.0^circ C 1.00 times 10^3 kg/m^3

A 0.300 kg sample is placed in a cooling apparatus that removes energy as heat at a constant rate of 2.81 W. Figure 18?52 gives the temperature T of the sample versus time t. The temperature scale is set by \(T_{s}=30^{\circ} \mathrm{C}\) and the time scale is set by \(t_{s}=20\) min. What is the specific heat of the sample? Text Transcription: T_s = 30^circ C t_s=20

The average rate at which energy is conducted outward through the ground surface in North America is \(54.0 \mathrm{mW} / \mathrm{m}^{2}\), and the average thermal conductivity of the near-surface rocks is \(2.50 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}\). Assuming a surface temperature of \(10.0^{\circ} \mathrm{C}\), find the temperature at a depth of 35.0 km (near the base of the crust). Ignore the heat generated by the presence of radioactive elements. Text Transcription: 54.0 mW/m^2 2.50 W/m cdot K 10.0^circ C

What is the volume increase of an aluminum cube 5.00 cm on an edge when heated from \(10.0^{\circ} \mathrm{C} \text { to } 60.0^{\circ} \mathrm{C}\)? Text Transcription: 10.0^circ C to 60.0^circ C

In a series of experiments, block B is to be placed in a thermally insulated container with block A, which has the same mass as block B. In each experiment, block B is initially at a certain temperature \(T_{B}\), but temperature \(T_{A}\) of block A is changed from experiment to experiment. Let \(T_{f}\) represent the final temperature of the two blocks when they reach thermal equilibrium in any of the experiments. Figure 18-53 gives temperature \(T_{f}\) versus the initial temperature \(T_{A}\) for a range of possible values of \(T_{A}\), from \(T_{A 1}\) = 0 K to \(T_{A 2}\) = 500 K. The vertical axis scale is set by \(T_{f s}\) = 400 K. What are (a) temperature \(T_{B}\) and (b) the ratio \(c_{B}/c_{A}\) of the specific heats of the blocks? Text Transcription: T_B T_A T_f T_A1 T_A2 T_fs c_B/c_A

Figure 18-54 displays a closed cycle for a gas. From c to b, 40 J is transferred from the gas as heat. From b to a, 130 J is transferred from the gas as heat, and the magnitude of the work done by the gas is 80 J. From a to c, 400 J is transferred to the gas as heat. What is the work done by the gas from a to c? (Hint: You need to supply the plus and minus signs for the given data.)

Three equal-length straight rods, of aluminum, Invar, and steel, all at \(20.0^{\circ} \mathrm{C}\), form an equilateral triangle with hinge pins at the vertices. At what temperature will the angle opposite the Invar rod be \(59.95^{\circ}\)? See Appendix E for needed trigonometric formulas and Table 18-2 for needed data. Text Transcription: 20.0^circ C 59.95^circ

The temperature of a 0.700 kg cube of ice is decreased to \(-150^{\circ} \mathrm{C}\). Then energy is gradually transferred to the cube as heat while it is otherwise thermally isolated from its environment. The total transfer is 0.6993 MJ. Assume the value of \(c_{\text {ice }}\) given in Table 18-3 is valid for temperatures from \(-150^{\circ} \mathrm{C} \text { to } 0^{\circ} \mathrm{C}\). What is the final temperature of the water? Text Transcription: -150^circ C c_ice -150^circ C to 0^circ C

Icicles. Liquid water coats an active (growing) icicle and extends up a short, narrow tube along the central axis (Fig. 18-55). Because the water–ice interface must have a temperature of \(0^{\circ} \mathrm{C}\), the water in the tube cannot lose energy through the sides of the icicle or down through the tip because there is no temperature change in those directions. It can lose energy and freeze only by sending energy up (through distance L) to the top of the icicle, where the temperature \(T_{r}\) can be below \(0^{\circ} \mathrm{C}\). Take L = 0.12 m and \(T_{r}=-5^{\circ} \mathrm{C}\). Assume that the central tube and the upward conduction path both have cross-sectional area A. In terms of A, what rate is (a) energy conducted upward and (b) mass converted from liquid to ice at the top of the central tube? (c) At what rate does the top of the tube move downward because of water freezing there? The thermal conductivity of ice is \(0.400 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}\), and the density of liquid water is 1000 \(\mathrm{kg} / \mathrm{m}^{3}\). Text Transcription: 0^circ C T_r T_r = -5^circ C 0.400 W/m cdot K kg/m^3

A sample of gas expands from an initial pressure and volume of 10 Pa and \(1.0 \mathrm{m}^{3}\) to a final volume of \(2.0 \mathrm{m}^{3}\). During the expansion, the pressure and volume are related by the equation \(p=a V^{2}\), where a = 10 \(\mathrm{N} / \mathrm{m}^{8}\). Determine the work done by the gas during this expansion. Text Transcription: 1.0 m^3 2.0 m^3 p = aV^2 N/m^8

Figure 18-56a shows a cylinder containing gas and closed by a movable piston. The cylinder is kept submerged in an ice–water mixture. The piston is quickly pushed down from position 1 to position 2 and then held at position 2 until the gas is again at the temperature of the ice–water mixture; it then is slowly raised back to position 1. Figure 18-56b is a p-V diagram for the process. If 100 g of ice is melted during the cycle, how much work has been done on the gas?

A sample of gas undergoes a transition from an initial state a to a final state b by three different paths (processes), as shown in the p-V diagram in Fig. 18-57, where \(V_{b}=5.00 V_{i}\). The energy transferred to the gas as heat in process 1 is \(10 p_{i} V_{i}\). In terms of \(p_{i} V_{i}\), what are (a) the energy transferred to the gas as heat in process 2 and (b) the change in internal energy that the gas undergoes in process 3? Text Transcription: V_b = 5.00V_i 10p_i V_i p_i V_i

The temperature of a Pyrex disk is changed from \(10.0^{\circ} \mathrm{C} \text { to } 60.0^{\circ} \mathrm{C}\). Its initial radius is 8.00 cm; its initial thickness is 0.500 cm. Take these data as being exact. What is the change in the volume of the disk? (See Table 18-2.) Text Transcription: 10.0^circ C to 60.0^circ C

(a) Calculate the rate at which body heat is conducted through the clothing of a skier in a steady-state process, given the following data: the body surface area is \(1.8 \mathrm{m}^{2}\), and the clothing is 1.0 cm thick; the skin surface temperature is \(33^{\circ} \mathrm{C}\) and the outer surface of the clothing is at \(1.0^{\circ} \mathrm{C}\); the thermal conductivity of the clothing is \(0.040 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}\). (b) If, after a fall, the skier’s clothes became soaked with water of thermal conductivity \(0.60 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}\), by how much is the rate of conduction multiplied? Text Transcription: 1.8 m^2 33^circ C 1.0^circ C 0.040 W/m cdot K 0.60 W/m cdot K

A 2.50 kg lump of aluminum is heated to \(92.0^{\circ} \mathrm{C}\) and then dropped into 8.00 kg of water at \(5.00^{\circ} \mathrm{C}\). Assuming that the lump– water system is thermally isolated, what is the system’s equilibrium temperature? Text Transcription: 92.0^circ C 5.00^circ C

A glass window pane is exactly 20 cm by 30 cm at \(10^{\circ} \mathrm{C}\). By how much has its area increased when its temperature is\(40^{\circ} \mathrm{C}\), assuming that it can expand freely? Text Transcription: 10^circ C 40^circ C

A recruit can join the semi-secret “300 F” club at the Amundsen– Scott South Pole Station only when the outside temperature is below \(-70^{\circ} \mathrm{C}\). On such a day, the recruit first basks in a hot sauna and then runs outside wearing only shoes. (This is, of course, extremely dangerous, but the rite is effectively a protest against the constant danger of the cold.) Assume that upon stepping out of the sauna, the recruit’s skin temperature is \(102^{\circ} \mathrm{F}\) and the walls, ceiling, and floor of the sauna room have a temperature of \(30^{\circ} \mathrm{C}\). Estimate the recruit’s surface area, and take the skin emissivity to be 0.80. (a) What is the approximate net rate \(P_{\text {net }}\) at which the recruit loses energy via thermal radiation exchanges with the room? Next, assume that when outdoors, half the recruit’s surface area exchanges thermal radiation with the sky at a temperature of \(-25^{\circ} \mathrm{C}\) and the other half exchanges thermal radiation with the snow and ground at a temperature of \(-80^{\circ} \mathrm{C}\). What is the approximate net rate at which the recruit loses energy via thermal radiation exchanges with (b) the sky and (c) the snow and ground? Text Transcription: -70^circ C 102^circ F 30^circ C P_net -25^circ C -80^circ C

A steel rod at \(25.0^{\circ} \mathrm{C}\) is bolted at both ends and then cooled. At what temperature will it rupture? Use Table 12-1. Text Transcription: 25.0^circ C

Soon after Earth was formed, heat released by the decay of radioactive elements raised the average internal temperature from 300 to 3000 K, at about which value it remains today. Assuming an average coefficient of volume expansion of \(3.0 \times 10^{-5} \mathrm{K}^{-1}\), by how much has the radius of Earth increased since the planet was formed? Text Transcription: 3.0 times 10^-5 K^-1

A rectangular plate of glass initially has the dimensions 0.200 m by 0.300 m. The coefficient of linear expansion for the glass is \(9.00 \times 10^{-6} / \mathrm{K}\). What is the change in the plate’s area if its temperature is increased by 20.0 K? Text Transcription: 9.00 times 10^-6/K

Suppose that you intercept \(5.0 \times 10^{-3}\) of the energy radiated by a hot sphere that has a radius of 0.020 m, an emissivity of 0.80, and a surface temperature of 500 K. How much energy do you intercept in 2.0 min? Text Transcription: 5.0 times 10^-3

A thermometer of mass 0.0550 kg and of specific heat \(0.837 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}|) reads \(15.0^{\circ} \mathrm{C}\). It is then completely immersed in 0.300 kg of water, and it comes to the same final temperature as the water. If the thermometer then reads \(44.4^{\circ} \mathrm{C}\), what was the temperature of the water before insertion of the thermometer? Text Transcription: 0.837 kJ/kg cdot K 15.0^circ C 44.4^circ C

A sample of gas expands from \(V_{1}=1.0 \mathrm{m}^{3} \text { and } p_{1}=40 \mathrm{Pa}\) to \(V_{2}=4.0 \mathrm{m}^{3} \quad \text { and } \quad p_{2}=10 \mathrm{Pa}\) along path B in the p-V diagram in Fig. 18-58. It is then compressed back to \(V_{1}\) along either path A or path C. Compute the net work done by the gas for the complete cycle along (a) path BA and (b) path BC. Text Transcription: V_1 = 1.0 m^3 and p_1 = 40 Pa V_2 = 4.0 m^3 and p_2 = 10 Pa V_1

Figure 18-59 shows a composite bar of length \(L=L_{1}+L_{2}\) and consisting of two materials. One material has length \(L_{1}\) and coefficient of linear expansion \(\alpha_{1}\); the other has length L_{2} and coefficient of linear expansion \(\alpha_{2}\). (a) What is the coefficient of linear expansion \(\alpha\) for the composite bar? For a particular composite bar, L is 52.4 cm, material 1 is steel, and material 2 is brass. If \(\alpha=1.3 \times 10^{-5} / \mathrm{C}^{c}\), what are the lengths (b) \(L_{1}\) and (c) \(L_{2}\)? Text Transcription: L = L_1+L_2 L_1 alpha_1 L_2 alpha_2 alpha alpha = 1.3 times 10^-5/C^c

On finding your stove out of order, you decide to boil the water for a cup of tea by shaking it in a thermos flask. Suppose that you use tap water at \(19^{\circ} \mathrm{C}\), the waterfalls 32 cm each shake, and you make 27 shakes each minute. Neglecting any loss of thermal energy by the flask, how long (in minutes) must you shake the flask until the water reaches \(100^{\circ} \mathrm{C}\)? Text Transcription: 19^circ C 100^circ C

The p-V diagram in Fig. 18-60 shows two paths along which a sample of gas can be taken from state a to state b, where \(V_{b}=3.0 V_{1}\). Path 1 requires that energy equal to \(5.0 p_{1} V_{1}\) be transferred to the gas as heat. Path 2 requires that energy equal to \(5.5 p_{1} V_{1} be transferred to the gas as heat. What is the ratio \(p_{2} / p_{1}\)? Text Transcription: V_b = 3.0 V_1 5.0p_1 V_1 5.5p_1 V_1 p_2/p_1

A cube of edge length \(6.0 \times 10^{-6}\) m, emissivity 0.75, and temperature \(-100^{\circ} \mathrm{C}\) floats in an environment at \(-150^{\circ} \mathrm{C}\). What is the cube’s net thermal radiation transfer rate? Text Transcription: 6.0 times 10^-6 -100^circ C -150^circ C

A flow calorimeter is a device used to measure the specific heat of a liquid. Energy is added as heat at a known rate to a stream of the liquid as it passes through the calorimeter at a known rate. Measurement of the resulting temperature difference between the inflow and the outflow points of the liquid stream enables us to compute the specific heat of the liquid. Suppose a liquid of density \(0.85 \mathrm{g} / \mathrm{cm}^{3}\) flows through a calorimeter at the rate of \(8.0 \mathrm{cm}^{3} / \mathrm{s}\). When energy is added at the rate of 250 W by means of an electric heating coil, a temperature difference of \(15 \mathrm{C}^{\circ}\) is established in steady-state conditions between the inflow and the outflow points. What is the specific heat of the liquid? Text Transcription: 0.85 g/cm^3 8.0 cm^3/s 15 C^circ

An object of mass 6.00 kg falls through a height of 50.0 m and, by means of a mechanical linkage, rotates a paddle wheel that stirs 0.600 kg of water. Assume that the initial gravitational potential energy of the object is fully transferred to thermal energy of the water, which is initially at \(15.0^{\circ} \mathrm{C}\). What is the temperature rise of the water? Text Transcription: 15.0^circ C

The Pyrex glass mirror in a telescope has a diameter of 170 in. The temperature ranges from \(-16^{\circ} \mathrm{C} \text { to } 32^{\circ} \mathrm{C}\) on the location of the telescope. What is the maximum change in the diameter of the mirror, assuming that the glass can freely expand and contract? Text Transcription: -16^circ C to 32^circ C

The area A of a rectangular plate is ab = 1.4 \(\mathrm{m}^{2}\). Its coefficient of linear expansion is \(\alpha=32 \times 10^{-6} / \mathrm{C}^{4}\). After a temperature rise \(\Delta T=89^{\circ} \mathrm{C}\), side a is longer by \(\Delta a\) and side b is longer by \(\Delta b\) (Fig. 18-61). Neglecting the small quantity \((\Delta a \Delta b) / ab\), find \(\Delta A\). Text Transcription: m^2 alpha = 32 times 10^-6/C^4 Delta T = 89^circ C Delta a Delta b (Delta a Delta b)/ab Delta A

Consider the liquid in a barometer whose coefficient of volume expansion is \(6.6 \times 10^{-4} / \mathrm{C}^{\circ}\). Find the relative change in the liquid’s height if the temperature changes by \(12 \mathrm{C}^{\mathrm{c}}\) while the pressure remains constant. Neglect the expansion of the glass tube. Text Transcription: 6.6 times 10^-4/C^circ 12 C^mathrmc

A pendulum clock with a pendulum made of brass is designed to keep accurate time at \(23^{\circ} \mathrm{C}\). Assume it is a simple pendulum consisting of a bob at one end of a brass rod of negligible mass that is pivoted about the other end. If the clock operates at \(0.0^{\circ} \mathrm{C}\), (a) does it run too fast or too slow, and (b) what is the magnitude of its error in seconds per hour? Text Transcription: 23^circ C 0.0^circ C

Materials A, B, and C are solids that are at their melting temperatures. Material A requires 200 J to melt 4 kg, material B requires 300 J to melt 5 kg, and material C requires 300 J to melt 6 kg. Rank the materials according to their heats of fusion, greatest first.

A sample A of liquid water and a sample B of ice, of identical mass, are placed in a thermally insulated container and allowed to come to thermal equilibrium. Figure 18-25a is a sketch of the temperature T of the samples versus time t. (a) Is the equilibrium temperature above, below, or at the freezing point of water? (b) In reaching equilibrium, does the liquid partly freeze, fully freeze, or undergo no freezing? (c) Does the ice partly melt, fully melt, or undergo no melting?

For which cycle in Fig. 18-27, traversed clockwise, is (a) W greater and (b) Q greater?

A solid cube of edge length r, a solid sphere of radius r, and a solid hemisphere of radius r, all made of the same material, are maintained at temperature 300 K in an environment at temperature 350 K. Rank the objects according to the net rate at which thermal radiation is exchanged with the environment, greatest first.

Icebergs in the North Atlantic present hazards to shipping, causing the lengths of shipping routes to be increased by about 30% during the iceberg season. Attempts to destroy icebergs include planting explosives, bombing, torpedoing, shelling, ramming, and coating with black soot. Suppose that direct melting of the iceberg, by placing heat sources in the ice, is tried. How much energy as heat is required to melt 10% of an iceberg that has a mass of 200 000 metric tons? (Use 1 metric ton = 1000 kg.)

A copper rod, an aluminum rod, and a brass rod, each of 6.00 m length and 1.00 cm diameter, are placed end to end with the aluminum rod between the other two. The free end of the copper rod is maintained at water’s boiling point, and the free end of the brass rod is maintained at water’s freezing point. What is the steady-state temperature of (a) the copper–aluminum junction and (b) the aluminum–brass junction?

An athlete needs to lose weight and decides to do it by “pumping iron.” (a) How many times must an 80.0 kg weight be lifted a distance of 1.00 m in order to burn off 1.00 lb of fat, assuming that that much fat is equivalent to 3500 Cal? (b) If the weight is lifted once every 2.00 s, how long does the task take?

It is possible to melt ice by rubbing one block of it against another. How much work, in joules, would you have to do to get 1.00 g of ice to melt?

A room is lighted by four 100 W incandescent light bulbs. (The power of 100 W is the rate at which a bulb converts electrical energy to heat and the energy of visible light.) Assuming that 73% of the energy is converted to heat, how much heat does the room receive in 6.9 h?

An energetic athlete can use up all the energy from a diet of 4000 Cal/day. If he were to use up this energy at a steady rate, what is the ratio of the rate of energy use compared to that of a 100 W bulb? (The power of 100 W is the rate at which the bulb converts electrical energy to heat and the energy of visible light.)

A 1700 kg Buick moving at 83 km/h brakes to a stop, at uniform deceleration and without skidding, over a distance of 93 m. At what average rate is mechanical energy transferred to thermal energy in the brake system?