Concepts & Calculations

Note: Each of these problems consists of Concept Questions followed by a related quantitative Problem. The Concept Questions involve little or no mathematics. They focus on the concepts with which the problems deal. Recognizing the concepts is the essential initial step in any problem-solving technique.

| 95 | Concept Questions The drawing shows two thermometers, A and B, whose temperatures are measured in °A and °B. The ice and boiling points of water are also indicated. (a) Is the size of one degree on the A scale larger than, the same as, or smaller than on the B scale? Why? (b) Is a given temperature on the A scale (e.g., +20 °A) hotter than, the same as, or colder than the same reading on the B scale (e.g., +20 °B)? Provide a reason for your answer.
Problem (a) Using the data in the drawing, determine the number of B° on the B scale that correspond to 1 A° on the A scale. (b) If the temperature of a substance reads +40.0 °A on the A scale, what would that temperature read on the B scale?

| 96 | Concept Questions (a) When an object, such as a rod, is heated, what factors determine how much its length increases? (b) Suppose two rods are made from materials that have different coefficients of linear expansion, but their lengths change by the same amount when their temperatures change by the same amount. Are their initial lengths the same or different? Explain.
Problem One rod is made from lead and another from quartz. They are heated and experience the same change in temperature. If the initial length of the lead rod is 0.10 m, what is the initial length of the quartz rod? Be sure that your answer is consistent with your answer to the Concept Questions.

| 97 | Concept Questions An aluminum can is filled to the brim with a liquid. The can and the liquid are heated so their temperatures change by the same amount. (a) In general, what factors determine how the volume of an object changes when it is heated? (b) Aluminum has a smaller coefficient of volume expansion than the liquid does. Which, if either, will expand more, the can or the liquid? Provide a reason for your answer. (c) How is the volume of liquid that spills over related to the changes in the volume of the can and the liquid?
Problem The can’s initial volume at 5 °C is . The coefficient of volume expansion for aluminum is , according to Table 12-1. When the can and the liquid are heated to of liquid spills over. What is the coefficient of volume expansion of the liquid?

| 98 | Concept Questions (a) When heat is added to an object, what factors determine its change in temperature, assuming there is no phase change? (b) Suppose the same amount of heat is applied to two bars without their changing phase. They have the same mass, but experience different changes in temperature. Are the specific heat capacities the same for each bar? Why or why not?
Problem Two bars of identical mass are at 25 °C. One is made from glass and the other from another substance. When identical amounts of heat are supplied to each, the glass bar reaches a temperature of 88 °C, while the other reaches 250.0 °C. What is the specific heat capacity of the other substance?

| 99 | Concept Questions Suppose you have two solid objects, A and B, made from different materials. They have the same mass, and each solid is at its melting temperature. You then add heat to melt them. (a) It takes less heat to melt A than B. Which, if either, has the larger latent heat of fusion? Explain. (b) The mass of each is doubled. Does it require twice as much heat to melt them? Justify your answer.
Problem (a) Objects A and B have the same mass of 3.0 kg. They melt when of heat is added to A and is added to B. Determine the latent heats of fusion. ( b) Find the heat required to melt object A when its mass is 6.0 kg. Verify that your answers are consistent with your answers to the Concept Questions.

| 100 | Concept Questions On a cool autumn morning, the relative humidity is 100%. (a) Does this mean that the partial pressure of water in the air equals atmospheric pressure? Why or why not? (b) Suppose the air warms up in the afternoon, but the partial pressure of water in the air does not change. Is the humidity still 100%? Provide a reason for your answer.
Problem The vapor pressure of water at 20 °C is 2500 Pa. (a) What percentage of atmospheric pressure is this? (b) What percentage of the total air pressure at 20 °C is due to water vapor if the relative humidity is 100%? (c) The vapor pressure of water at 35 °C is 5500 Pa. What is the relative humidity at this temperature if the partial pressure of water in the air has not changed from that at 20 °C?

* | 101 | Concept Questions (a) A ball and a thin plate are made from different materials and have the same initial temperature. The ball does not fit through a hole in the plate, because the diameter of the ball is slightly larger than the diameter of the hole. However, the ball will pass through the hole when the ball and the plate are both heated to a common higher temperature. How do the coefficients of linear expansion of the ball and the plate compare? Explain. (b) The drawing shows three ball/plate arrangements like that in Concept Question (a). In each, the diameters of the balls are the same, and the diameters of the holes are the same. As the temperature increases, which ball falls through the hole first, which second, and which third? Account for your answers with the aid of data from Table 12-1.
Problem In each of the arrangements in the drawing the diameter of the ball is larger than the diameter of the hole, which has a diameter of 0.10 m. The initial temperature of each arrangement is 25.0 °C. At what temperature will the ball fall through the hole in each arrangement? Verify that your answer is consistent with your answer to Concept Question (b).

* | 102 | Concept Questions (a) Two portions of the same liquid have the same mass, but different temperatures. They are mixed in a container that prevents the exchange of heat with the environment. Portion A has the higher initial temperature of T0A, while portion B has an initial temperature of T0B. Relative to these two temperatures, where on the temperature scale will the final equilibrium temperature of the mixture be located? Explain. (b) Three portions of the same liquid are mixed in a container that prevents the exchange of heat with the environment. Portion A has a mass m and a temperature of 94.0 °C, portion B has a mass m and a temperature of 78.0 °C, and portion C has a mass 2m and a temperature of 34.0 °C. Considering your answer to Concept Question (a) and without doing a heat-lost-equals-heat-gained calculation, deduce the final temperature of the mixture at equilibrium. Justify your answer.
Problem Three portions of the same liquid are mixed in a container that prevents the exchange of heat with the environment. Portion A has a mass m and a temperature of 94.0 °C, portion B has a mass m and a temperature of 78.0 °C, and portion C has a mass mC and a temperature of 34.0 °C. What must be the mass of portion C such that the final temperature Tf of the three-portion mixture is Tf = 50.0 °C? Express your answer in terms of m; e.g., mC = 2.20m.

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