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Unformatted text preview: CHAPTER 12 TEMPERATURE AND HEAT ANSWERS TO FOCUS ON CONCEPTS QUESTIONS 1. (e) On each scale there are 100 degrees between the ice and steam points, so the size of the degree is the same on each scale. 2. (b) According to Equation 12.2, the change in length ∆ L of each rod is given by ∆ L = α L ∆ T , where α is the coefficient of linear expansion, L is the initial length, and ∆ T is the change in temperature. Since the initial length and the change in temperature are the same for each rod, the rod with the larger coefficient of linear expansion has the greater increase in length as the temperature rises. Thus, the aluminum rod lengthens more than the steel rod, so the rods will meet to the right of the midpoint. 3. 1.2 × 10 3 − cm 4. (d) In Arrangement I cooling allows the ball to pass through the hole. Therefore, the ball must shrink more than the hole, and the coefficient of linear thermal expansion of metal A must be greater than that of metal B. In Arrangement II heating allows the ball to pass through the hole. Therefore, the coefficient of linear thermal expansion of metal C must be greater than that of metal A. 5. (c) The gap expands as the temperature is increased, in a way similar to that of a hole when it expands according to the coefficient of linear thermal expansion of the surrounding material. In this case the surrounding material is copper. 6. (b) The change in volume ∆ V is given by Equation 12.3 as ∆ V = β V ∆ T , where β is the coefficient of volume thermal expansion, V is the initial volume, and ∆ T is the change in temperature. Since the sphere and the cube are made from the same material, the coefficient of volume expansion is the same for each. Moreover, the temperature change is the same for each. Therefore, the change in volume is proportional to the initial volume. The initial volume of the cube is greater, since the sphere would fit within the cube. Thus, the change in volume of the cube is greater. 7. (a) To keep the overflow to a minimum, the container should be made from a material that has the greatest coefficient of volume thermal expansion and filled with a liquid that has the smallest coefficient of volume thermal expansion. That way, when the full container is heated, the cavity holding the liquid will expand more and the liquid will expand less, both effects leading to a reduced amount of overflow. 8. 77 C° 115 TEMPERATURE AND HEAT 9. (e) The heat Q required to raise the temperature of a mass m of material by an amount ∆ T is given by Equation 12.4 as Q = cm ∆ T , where c is the specific heat capacity of the material. Since the material is the same in all cases, the specific heat capacity is the same. What matters is the product of m and ∆ T . Since this product is the same in all cases, the amount of heat needed is also the same....
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