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# Explain why an ideal gas taken around a rectangular PV

ISBN: 9780201380279 40

## Solution for problem 12P Chapter 4

An Introduction to Thermal Physics | 1st Edition

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Problem 12P

PROBLEM 12P

Explain why an ideal gas taken around a rectangular PV cycle, as considered in below Problem 1 and Problem 2, cannot be used (in reverse) for refrigeration.

Problem: 1

An ideal diatomic gas, in a cylinder with a movable piston, undergoes the rectangular cyclic process shown in below Figure. Assume that the temperature is always such that rotational degrees of freedom are active, but vibrational modes arc “frozen out.” Also assume that the only type of work done on the gas is quasistatic compression-expansion work.

(a) For each of the four steps A through D, compute the work done on the gas, the heat added Lo the gas, and the change in the energy content of the gas. Express all answers in terms of P1, P2, V1. and V2. (Hint: Compute ΔU before Q, using the ideal gas law and the equipartition theorem.)

(b) Describe in words what is physically being done during each of the four steps; for example, during step A, heat is added to the gas (from an external flame or something) while the piston is held fixed.

(c) Compute the net work done on the gas, the net heat added to the gas, and the net change in the energy of the gas during the entire cycle. Are the results as yon expected? Explain briefly.

Figure: PV Diagrams

Problem: 2

To measure the heat capacity of an object, all you usually have to do is put it in thermal contact with another object whose heat capacity you know. As an example, suppose that a chunk of metal is immersed in boiling water (100°C), then is quickly transferred into a Styrofoam cup containing 250 g of water at 20°C. After a minute or so, the temperature of the contents of the cup is 24°C. Assume that during this time no significant energy is transferred between the contents of the cup and the surroundings. The heat capacity of the cup itselfis negligible.

(a) How much heat is gained by the water?

(b) How much heat is lost by the metal?(c) What is the heat capacity of this chunk of metal?(d) If the mass of the chunk of metal is 100 g, what is its specific heat capacity?
Step-by-Step Solution:
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1/11/17 PHYS 202 The syllabus is online Chapter 11 Preview: The basic Energy Model  This chapter is about thermal energy, chemical energy, and energy transfers in the form of heat  Work and heat are energy transfers that change the system’s total energy. If the system is isolated, the total energy is conserved o If energy goes into the system from the environment,...

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##### ISBN: 9780201380279

An Introduction to Thermal Physics was written by and is associated to the ISBN: 9780201380279. Since the solution to 12P from 4 chapter was answered, more than 233 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 12P from chapter: 4 was answered by , our top Physics solution expert on 07/05/17, 04:29AM. This textbook survival guide was created for the textbook: An Introduction to Thermal Physics , edition: 1. This full solution covers the following key subjects: gas, heat, capacity, cup, during. This expansive textbook survival guide covers 10 chapters, and 454 solutions. The answer to “Explain why an ideal gas taken around a rectangular PV cycle, as considered in below and 2, cannot be used (in reverse) for refrigeration.Problem: 1An ideal diatomic gas, in a cylinder with a movable piston, undergoes the rectangular cyclic process shown in below Figure. Assume that the temperature is always such that rotational degrees of freedom are active, but vibrational modes arc “frozen out.” Also assume that the only type of work done on the gas is quasistatic compression-expansion work.(a) For each of the four steps A through D, compute the work done on the gas, the heat added Lo the gas, and the change in the energy content of the gas. Express all answers in terms of P1, P2, V1. and V2. (Hint: Compute ?U before Q, using the ideal gas law and the equipartition theorem.)________________(b) Describe in words what is physically being done during each of the four steps; for example, during step A, heat is added to the gas (from an external flame or something) while the piston is held fixed.________________(c) Compute the net work done on the gas, the net heat added to the gas, and the net change in the energy of the gas during the entire cycle. Are the results as yon expected? Explain briefly.Figure: PV Diagrams Problem: 2To measure the heat capacity of an object, all you usually have to do is put it in thermal contact with another object whose heat capacity you know. As an example, suppose that a chunk of metal is immersed in boiling water (100°C), then is quickly transferred into a Styrofoam cup containing 250 g of water at 20°C. After a minute or so, the temperature of the contents of the cup is 24°C. Assume that during this time no significant energy is transferred between the contents of the cup and the surroundings. The heat capacity of the cup itselfis negligible.(a) How much heat is gained by the water?________________(b) How much heat is lost by the metal?________________(c) What is the heat capacity of this chunk of metal?________________(d) If the mass of the chunk of metal is 100 g, what is its specific heat capacity?” is broken down into a number of easy to follow steps, and 357 words.

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