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.

| 93 | Concept Questions A system does of work, and of heat flows into the system in the process. (a) Considered by itself, does the work increase or decrease the internal energy of the system? (b) Considered by itself, does the heat increase or decrease the internal energy? (c) Considering the work and heat together, does the internal energy of the system increase, decrease, or remain the same? Explain.
Problem Find the change in the internal energy of the system. Make sure that your answer is consistent with your answers to the Concept Questions.

| 94 | Concept Questions A system gains a certain amount of energy in the form of heat at constant pressure, and the internal energy of the system increases by an even greater amount. (a) Is any work done and, if so, is it done on or by the system? (b) If there is work, is it positive or negative, according to our convention? (c) Does the volume of the system increase, decrease, or remain the same? Give your reasoning.
Problem A system gains 2780 J of heat at a constant pressure of , and its internal energy increases by 3990 J. What is the change in volume of the system, and is it an increase or a decrease? Verify that your answer is consistent with your answers to the Concept Questions.

| 95 | Concept Questions An ideal gas expands isothermally, doing work, while heat flows into the gas. (a) Does the internal energy of the gas increase, decrease, or remain the same? (b) Is the work done by the gas greater than, less than, or equal to the heat that flows into the gas? Account for your answers.
Problem Three moles of neon expand isothermally from 0.100 to 0.250 m3. Into the gas flows of heat. Assuming that neon is an ideal gas, find its temperature.

| 96 | Concept Questions A mountain climber, starting from rest, does work in climbing upward. At the if top, she is again at rest. In the process, her body generates of energy via metabolic processes. In fact, her body acts like a heat engine, the efficiency of which is given by Equation 15.11 as , where |W| is the magnitude of the work and |QH| is the magnitude the input heat. (a) Is the of energy equal to |W| or to |QH|? (b) How is the work done in climbing upward related to the vertical height of the climb? Explain.
Problem The vertical height of the climb is 730 m. The climber has a mass of 52 kg. Find her efficiency as a heat engine.

| 97 | Concept Questions Two Carnot engines, A and B, utilize the same hot reservoir, but engine A is less efficient than engine B. (a) Which engine produces more work for a given heat input? (b) Which engine has the lower cold-reservoir temperature? Give your reasoning.
Problem Carnot engine A has an efficiency of 0.60, and Carnot engine B has an efficiency of 0.80. Both engines utilize the same hot reservoir, which has a temperature of 650 K and delivers 1200 J of heat to each engine. Find the magnitude of the work produced by each engine and the temperatures of the cold reservoirs that they use. Check to see that your answers are consistent with your answers to the Concept Questions.

| 98 | Concept Questions Two Carnot air conditioners, A and B, are removing heat from different rooms. The outside temperature is the same for both, but the room temperatures are different. The room serviced by unit A is kept colder than the room serviced by unit B. The heat removed from both rooms is the same, (a) Which unit requires the greater amount of work? (b) Which unit deposits the greater amount of heat outside? Explain.
Problem The outside temperature is 309.0 K. The room serviced by unit A is kept at a temperature of 294.0 K, while the room serviced by unit B is kept at 301.0 K. The heat removed from either room is 4330 J. For both units, find the magnitude of the work required and the magnitude of the heat deposited outside. Verify that your answers are consistent with your answers to the Concept Questions.

| 99 | Concept Questions An ideal gas is taken through the three processes () shown in the drawing. In general, for each process the internal energy U of the gas can change, because heat can be added to or removed from the gas and work W can be done by the gas or on the gas. (a) For the process , is work done by the gas or on the gas? Why or why not? (b) For the process , suppose that the change in the internal energy of the gas and the work W are known. Is it then possible to determine the heat Q that has been added to or removed from the gas? If so, explain how this could be done. (c) For the process , is it possible to find the change in the internal energy of the gas if the change in the internal energies for the processes and are known? If so, specify how this could be done.

Problem For the three processes shown in the drawing, fill in the five missing entries in the following table.

Process |  | Q | W
| (b) | +561 J | (a)
| +4303 J | (c) | +2867 J
| (d) | (e) | −3740 J

| 100 | Concept Questions (a) A real (irreversible) engine operates between hot and cold reservoirs whose temperatures are TH and TC. The engine absorbs heat of magnitude |QH| from the hot reservoir and performs work of magnitude |W|. What is the expression that gives the change in entropy of the universe associated with the operation of this engine? Express your answer in terms of TH, TC, |QH|, and |QC|. (b) Would you expect the change in the entropy of the universe to be greater than, less than, or equal to zero? Provide a reason for your answer. (c) Suppose that a reversible engine (a Carnot engine) operates between the same hot and cold temperatures as the irreversible engine described above. For the same input heat |QH|, would the reversible engine produce more, less, or the same work as the irreversible engine? Justify your answer. (d) In terms of and TC, how could one determine the difference, if any, between the work done by the reversible engine and that done by the irreversible engine?
Problem (a) An irreversible engine operates between temperatures of 852 and 314 K. It absorbs 1285 J of heat from the hot reservoir and does 264 J of work. What is the change in the entropy of the universe associated with the operation of this engine? (b) If the engine were reversible, what is the magnitude |W| of the work it would have done, assuming it operated between the same temperatures and absorbed the same heat as the irreversible engine? (c) Using the results of parts (a) and (b), find the difference between the work produced by the reversible and irreversible engines.

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