SERWAY QUESTIONS and steam at one atmosphere of pressure?
SERWAY QUESTIONS 1. What is the temperature of a system in thermal equilibrium with another system made up of water and steam at one atmosphere of pressure? a. 0F b. 273 K c. 0 K d. 100C 2. The observation that materials expand in size with an increase in temperature can be applied to what proportion of existing substances? a. 100% b. most c. few d. none 3. A brass cube, 10 cm on a side, is raised in temperature by 200C. The coefficient of volume expansion of brass is 57 106/C. By what percentage is any one of the 10-cm edges increased in length? a. 4% b. 2.8% c. 0.38% d. 0.29% 4. An automobile gas tank is filled to its capacity of 15.00 gallons with the gasoline at an initial temperature of 10C. The automobile is parked in the sun causing the gasoline's temperature to rise to 60C. If the coefficient of volume expansion for gasoline is 9.6 104/C, what volume runs out the overflow tube? Assume the change in volume of the tank is negligible. a. 1.74 gallons b. 1.18 gallons c. 0.72 gallons d. 0.30 gallons 5. The thermal expansion of a solid is caused by: a. the breaking of bonds between atoms. b. increasing the amplitude of the atoms vibration. c. increasing the distance between equilibrium positions for the vibrating atoms. d. all of the above. 6. A steel sphere sits on top of an aluminum ring. The steel sphere ( = 1.10 105/C) has a diameter of 4.000 0 cm at 0C. The aluminum ring ( = 2.40 105/C) has an inside diameter of 3.994 0 cm at 0C. Closest to which temperature given will the sphere just fall through the ring? a. 462C b. 208C c. 116C d. 57.7C 7. Between 0 and 4C, the volume coefficient of expansion for water: a. is positive. b. is zero. c. is becoming less dense. d. is negative. 8.A long steel beam has a length of twenty-five meters on a cold day when the temperature is 0C. What is the length of the beam on a hot day when T = 40C? (steel = 1.1 105/C) a. 25.000 44 m b. 25.004 4 m c. 25.011 m d. 25.044 m 9. Suppose the ends of a 20-m-long steel beam are rigidly clamped at 0C to prevent expansion. The rail has a cross-sectional area of 30 cm2. What force does the beam exert when it is heated to 40C? (steel = 1.1 105/C, Ysteel = 2.0 1011 N/m2). a. 2.6 105 N b. 5.6 104 N c. 1.3 103 N d. 6.5 102 N 10. At room temperature, the coefficient of linear expansion for Pyrex glass is ____ that for ordinary glass. a. the same as b. more than c. less than d. stronger than PROBLEMS: 1) Two objects with different sizes, masses, and temperatures are placed in thermal contact. Choose the best answer: Energy travels (a) from the larger object to the smaller object (b) from the object with more mass to the one with less mass (c) from the object at higher temperature to the object at lower temperature. Choice (c). When two objects having different temperatures are in thermal contact, energy is transferred from the higher temperature object to the lower temperature object. As a result, the temperature of the hotter object decreases and that of the cooler object increases until thermal equilibrium is reached at some intermediate temperature. 2) A steel railroad track has a length of 30.000 m when the temperature is 0°C. What is its length on a hot day when the temperature is 40.0°C? (b) Suppose the track is nailed down so that it can’t expand. What stress results in the track due to the temperature change? 3) QUESTION 10.3 What happens to the tension of wires in a piano when the temperature decreases? 4) EXERCISE 10.3 What is the length of the same railroad track on a cold winter day when the temperature is 0°F? ANSWER 29.994 m 5) A circular copper ring at 20.0°C has a hole with an area of 9.980 cm2. What minimum temperature must it have so that it can be slipped onto a steel metal rod having a crosssectional area of 10.000 cm2? (b) Suppose the ring and the rod are heated simultaneously. What minimum change in temperature of both will allow the ring to be slipped onto the end of the rod? (Assume no significant change in the coefficients of linear expansion over this temperature range.) 6) QUESTION 10.4 If instead of heating the copper ring in part (a) the steel rod is cooled, would the magnitude of the required temperature change be larger, smaller, or the same? Why? (Don’t calculate it!) 7) EXERCISE 10.4 A steel ring with a hole having area of 3.990 cm2 is to be placed on an aluminum rod with crosssectional area of 4.000 cm2. Both rod and ring are initially at a temperature of 35.0°C. At what common temperature can the steel ring be slipped onto one end of the aluminum rod? ANSWER 261°C 8) If you quickly plunge a room-temperature mercury thermometer into very hot water, the mercury level will (a) go up briefly before reaching a final reading, (b) go down briefly before reaching a final reading, or (c) not change. Choice (b). The glass surrounding the mercury expands before the mercury does, causing the level of the mercury to drop slightly. The mercury rises after it begins to get warmer and approaches the temperature of the hot water, because its coeffi cient of expansion is greater than that for glass. 9) If you are asked to make a very sensitive glass thermometer, which of the following working fluids would you choose? (a) mercury (b) alcohol (c) gasoline (d) glycerin Choice (c). Gasoline has the highest coeffi cient of expansion so it undergoes the greatest change in volume per degree change in temperature. 10) Two spheres are made of the same metal and have the same radius, but one is hollow and the other is solid. The spheres are taken through the same temperature increase. Which sphere expands more? (a) solid sphere, (b) hollow sphere, (c) they expand by the same amount, or (d) not enough information to say. Choice (c). A cavity in a material expands in exactly the same way as if the cavity were filled with the surrounding material. Thus, both spheres will expand by the same amount. 11) Estimate the fractional change in the volume of Earth’s oceans due to an average temperature change of 1°C. (b) Use the fact that the average depth of the ocean is 4.00 3 103 m to estimate the change In depth. Note that bwater 5 2.07 3 1024(°C)21. 12) QUESTION 10.5 Assuming all have the same initial volume, rank the following substances by the amount of volume expansion due to an increase in temperature, from least to most: glass, mercury, aluminum, ethyl alcohol. 13) EXERCISE 10.5 A 1.00-liter aluminum cylinder at 5.00°C is filled to the brim with gasoline at the same temperature. If the aluminum and gasoline are warmed to 65.0°C, how much of the gasoline spills out? Hint: Be sure to account for the expansion of the container. Also, ignore the possibility of evaporation, and assume the volume coefficients are good to three digits. ANSWER The volume spilled is 53.3 cm3. Forgetting to take into account the expansion of the cylinder results in a (wrong) answer of 57.6 cm3. 14) Why doesn’t the melting of ocean-based ice raise as much concern as the melting of land-based ice? Unlike land-based ice, ice fl oating in the ocean already displaces a quantity of liquid water whose weight equals the weight of the ice. This is the same situation as will exist after the ice melts, so the melting ocean-based ice will not change ocean levels much. 15) A grandfather clock is controlled by a swinging brass pendulum that is 1.3 m long at a temperature of 20°C. (a) What is the length of the pendulum rod when the temperature drops to 0.0°C? (b) If a pendulum’s period is given by T 5 2p!L/g , where L is its length, does the change in length of the rod cause the clock to run fast or slow? 16) A pair of eyeglass frames are made of epoxy plastic (coefficient of linear expansion 5 1.30 3 1024 °C21). At room temperature (20.0°C), the frames have circular lens holes 2.20 cm in radius. To what temperature must the frames be heated if lenses 2.21 cm in radius are to be inserted into them? 17) A spherical steel ball bearing has a diameter of 2.540 cm at 25.00°C. (a) What is its diameter when its temperature is raised to 100.0°C? (b) What temperature change is required to increase its volume by 1.000%? 18) An underground gasoline tank can hold 1.00 3 103 gallons of gasoline at 52.0°F. If the tank is being filled on a day when the outdoor temperature (and the gasoline in a tanker truck) is 95.0°F, how many gallons from the truck can be poured into the tank? Assume the temperature of the gasoline quickly cools from 95.0°F to 52.0°F upon entering the tank. 19) Show that the coefficient of volume expansion, b, is related to the coefficient of linear expansion, a, through the expression b 5 3a. 20) A hollow aluminum cylinder 20.0 cm deep has an internal capacity of 2.000 L at 20.0°C. It is completely filled with turpentine at 20.0°C. The turpentine and the aluminum cylinder are then slowly warmed together to 80.0°C. (a) How much turpentine overflows? (b) What is the volume of the turpentine remaining in the cylinder at 80.0°C? (c) If the combination with this amount of turpentine is then cooled back to 20.0°C, how far below the cylinder’s rim does the turpentine’s surface recede? 21) A construction worker uses a steel tape to measure the length of an aluminum support column. If the measured length is 18.700 m when the temperature is 21.2°C, what is the measured length when the temperature rises to 29.4°C? Note: Don’t neglect the expansion of the tape. Let L be the fi nal length of the aluminum column. This will also be the fi nal length of the quantity of tape now stretching from one end of the column to the other. In order to determine what the scale reading now is, we need to fi nd the initial length this quantity of tape had at 21.2°C (when the scale markings were presumably put on the tape).
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