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Unformatted text preview: CHAPTER 15 THERMODYNAMICS ANSWERS TO FOCUS ON CONCEPTS QUESTIONS ____________________________________________________________________________________________ 1. (c) This sign convention for Q and W is discussed in Section 15.3 (see, in particular, Equation 15.1). 2. U = - 9.3 10 5 J 3. (c) According to the discussion in Section 15.4, the area under a pressure- volume graph is the work W for any kind of process. Since the graph shows the gas being compressed, work is done on the gas. 4. (b) The work done by a gas is the area under the pressure-volume graph. The areas under curves A and B are the same (4 squares each), and each is greater than that under curve C (3 squares). 5. W = +1.2 10 5 J 6. (a) The first law of thermodynamics states that the heat Q is related to the change U in the internal energy and the work W by Q = U + W . Since all three paths start at A and end at B, the change in the internal energy of each gas is the same. Therefore, the path that involves the greatest amount of work is the one that has greatest amount of heat added to the gas. The drawing shows that the work (which is the area under the pressure-volume graph) is greatest for path 1 and smallest for path 3. 7. (e) The first law of thermodynamics, Q = ( U B- U A ) + W , can be used to find the heat Q , since U B and U A are given and W is the area under the pressure-volume graph. 8. (e) The internal energy of a monatomic ideal gas depends directly on its temperature (see Equation 14.7). In an isothermal process the temperature does not change. Therefore, the internal energy of the gas does not change. 9. W = - 1.81 10 4 J 10. (c) The temperature of the gas increases when its internal energy increases. According to the first law of thermodynamics, U = Q- W . Both heat and work can change the internal energy and, hence, the temperature of the gas. If Q = 0 J, U can still increase if W is a negative number, which means that work is done on the gas. 253 THERMODYNAMICS 11. (d) The work done on a monatomic gas during an adiabatic compression is given by (See Equation 15.4) ( 29 3 i f 2 W nR T T =- . 12. (a) The change in temperature is greatest when the change U in the internal energy of the gas is greatest. According to the first law of thermodynamics, U = Q- W , the change in the internal energy is greatest when heat Q is added and no work ( W = 0 J) is done by the gas. The gas does no work when its volume remains constant, so its change in temperature is greater than if the volume had changed. 13. (c) A more-efficient engine produces more work from the same amount of input heat, as expressed by W = eQ H (Equation 15.11). Part of the heat Q H from the hot reservoir is used to perform work W , and the remainder Q C is rejected to the cold reservoir. The conservation of energy states that Q H = W + Q C (Equation 15.12). If Q H is constant and W increases, the heat Q C must decrease....
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