Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
9th Edition
ISBN: 9781305372337
Author: Raymond A. Serway | John W. Jewett
Publisher: Cengage Learning
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Chapter 21, Problem 70AP
To determine
Prove that the slope of the adiabatic curve is steeper than the slope of the isothermal.
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Problem 3:
19.8 .
Figure E19.8 shows a pV-diagram for an ideal gas in
which its absolute temperature at b is one-fourth of its absolute
temperature at a. (a) What volume does this gas occupy at point b?
(b) How many joules of work was done by or on the gas in this
process? Was it done by or on the gas? (c) Did the internal energy
of the gas increase or decrease from a to b? How do you know?
(d) Did heat enter or leave the gas from a to b? How do you know?
Figure E19.8
p (atm)
b
a
1.50
V (L)
0.500
The temperature of 10 moles of an ideal gas is 1000 K. Compute the work done by the gas when it expands isothermally to three times its initial volume.
Given: Boltzmann constant: k = 1.38 x 10–23 J/K, Ideal Gas Constant: R = 8.31 J/(mol K)
A. 91300 J
B. 9130 J
C. 913 J
D. 91 J
E. 9 J
Question 1. An ideal diatomic gas contracts from 1.25 m³ to 0.500 m³ at a
constant pressure of 1.50 x 10°P.. Draw a PV diagram and name this process that
occurs at constant pressure. If the initial temperature is 425 K, calculate
(a) the work done on the gas,
(b) the change in internal energy of the gas,
(c) the energy transfer, Q, and,
(d) the final temperature.
Chapter 21 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
Ch. 21.1 - Two containers hold an ideal gas at the same...Ch. 21.2 - (i) How does the internal energy of an ideal gas...Ch. 21.3 - Prob. 21.3QQCh. 21.3 - Prob. 21.4QQCh. 21 - Prob. 1OQCh. 21 - Prob. 2OQCh. 21 - Prob. 3OQCh. 21 - Prob. 4OQCh. 21 - Prob. 5OQCh. 21 - Prob. 6OQ
Ch. 21 - Prob. 7OQCh. 21 - Prob. 8OQCh. 21 - Prob. 9OQCh. 21 - Prob. 1CQCh. 21 - Prob. 2CQCh. 21 - Prob. 3CQCh. 21 - Prob. 4CQCh. 21 - Prob. 5CQCh. 21 - Prob. 6CQCh. 21 - Prob. 7CQCh. 21 - Prob. 1PCh. 21 - Prob. 2PCh. 21 - Prob. 3PCh. 21 - Prob. 4PCh. 21 - A spherical balloon of volume 4.00 103 cm3...Ch. 21 - A spherical balloon of volume V contains helium at...Ch. 21 - A 2.00-mol sample of oxygen gas is confined to a...Ch. 21 - Prob. 8PCh. 21 - Prob. 9PCh. 21 - Prob. 10PCh. 21 - A 5.00-L vessel contains nitrogen gas at 27.0C and...Ch. 21 - A 7.00-L vessel contains 3.50 moles of gas at a...Ch. 21 - In a period of 1.00 s, 5.00 1023 nitrogen...Ch. 21 - In a constant-volume process, 209 J of energy is...Ch. 21 - Prob. 15PCh. 21 - Prob. 16PCh. 21 - Prob. 17PCh. 21 - A vertical cylinder with a heavy piston contains...Ch. 21 - Calculate the change in internal energy of 3.00...Ch. 21 - Prob. 20PCh. 21 - Prob. 21PCh. 21 - A certain molecule has f degrees of freedom. Show...Ch. 21 - Prob. 23PCh. 21 - Why is the following situation impossible? A team...Ch. 21 - Prob. 25PCh. 21 - Prob. 26PCh. 21 - During the compression stroke of a certain...Ch. 21 - Prob. 28PCh. 21 - Air in a thundercloud expands as it rises. If its...Ch. 21 - Prob. 30PCh. 21 - Prob. 31PCh. 21 - Prob. 32PCh. 21 - Prob. 33PCh. 21 - Prob. 34PCh. 21 - Prob. 35PCh. 21 - Prob. 36PCh. 21 - Prob. 37PCh. 21 - Prob. 38PCh. 21 - Prob. 39PCh. 21 - Prob. 40PCh. 21 - Prob. 41PCh. 21 - Prob. 42PCh. 21 - Prob. 43PCh. 21 - Prob. 44APCh. 21 - Prob. 45APCh. 21 - The dimensions of a classroom are 4.20 m 3.00 m ...Ch. 21 - The Earths atmosphere consists primarily of oxygen...Ch. 21 - Prob. 48APCh. 21 - Prob. 49APCh. 21 - Prob. 50APCh. 21 - Prob. 51APCh. 21 - Prob. 52APCh. 21 - Prob. 53APCh. 21 - Prob. 54APCh. 21 - Prob. 55APCh. 21 - Prob. 56APCh. 21 - Prob. 57APCh. 21 - In a cylinder, a sample of an ideal gas with...Ch. 21 - As a 1.00-mol sample of a monatomic ideal gas...Ch. 21 - Prob. 60APCh. 21 - Prob. 61APCh. 21 - Prob. 62APCh. 21 - Prob. 63APCh. 21 - Prob. 64APCh. 21 - Prob. 65APCh. 21 - Prob. 66APCh. 21 - Prob. 67APCh. 21 - Prob. 68APCh. 21 - Prob. 69APCh. 21 - Prob. 70APCh. 21 - Prob. 71APCh. 21 - Prob. 72APCh. 21 - Prob. 73APCh. 21 - Prob. 74CPCh. 21 - Prob. 75CP
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- Figure P21.37 shows a PV diagram for a gas that is compressed from Vi to Vf. Find the work done by the a. gas and b. environment during this process. Does energy enter the system or leave the system as a result of work? FIGURE P21.37arrow_forwardIn Figure P19.22, the change in internal energy of a gas that is taken from A to C along the blue path is +800 J. The work done on the gas along the red path ABC is 500 J. (a) How much energy must be added to the system by heat as it goes from A through B to C? (b) If the pressure at point A is five times that of point C, what is the work done on the system in going from C to D? Figure P19.22 (c) What is the energy exchanged with the surroundings by heat as the gas goes from C to A along the green path? (d) If the change in internal energy in going from point D to point A is +500 J, how much energy must be added to the system by heat as it goes from point C to point D?arrow_forwardThe arrow OA in the PV diagram shown in Figure OQ22.11 represents a reversible adiabatic expansion of an ideal gas. The same sample of gas, starting from the same state O. now undergoes an adiabatic free expansion to the same final volume. What point on the diagram could represent the final state of the gas? (a) the same point A as for the reversible expansion (b) point B (c) point C (d) any of those choices (e) none of those choicesarrow_forward
- Figure P21.45 shows a cyclic process ABCDA for 1.00 mol of an ideal gas. The gas is initially at Pi = 1.50 105 Pa, Vi = 1.00 103 m3 (point A in Fig. P21.45). a. What is the net work done on the gas during the cycle? b. What is the net amount of energy added by heat to this gas during the cycle? FIGURE P21.45arrow_forwardA 2.00-mol sample of a diatomic ideal gas expands slowly and adiabatically from a pressure of 5.00 atm and a volume of 12.0 L to a final volume of 30.0 L. (a) What is the final pressure of the gas? (b) What are the initial and final temperatures? Find (c) Q, (d) Eint, and (e) W for the gas during this process.arrow_forward(a) Determine the work done on a gas that expands from i to f as indicated in Figure P19.16. (b) What If? How much work is done on the gas if it is compressed from f to i along the same path? Figure P19.16arrow_forward
- You have a particular interest in automobile engines, so you have secured a co-op position at an automobile company while you attend school. Your supervisor is helping you to learn about the operation of an internal combustion engine. She gives you the following assignment, related to a simulation of a new engine she is designing. A gas, beginning at PA = 1.00 atm, VA = 0.500 L, and TA = 27.0C, is compressed from point A on the PV diagram in Figure P19.31 (page 530) to point B. This represents the compression stroke in a fourcycle gasoline engine. At that point, 132 J of energy is delivered to the gas at constant volume, taking the gas to point C. This represents the transformation of potential energy in the gasoline to internal energy when the spark plug fires. Your supervisor tells you that the internal energy of a gas is proportional to temperature (as we shall find in Chapter 20), the internal energy of the gas at point A is 200 J, and she wants to know what the temperature of the gas is at point C. Figure P19.31arrow_forwardIf a gas is compressed isothermally, which of the following statements is true? (a) Energy is transferred into the gas by heat. (b) No work is done on the gas. (c) The temperature of the gas increases. (d) The internal energy of the gas remains constant. (e) None of those statements is true.arrow_forwardFigure P21.36 shows a cyclic thermodynamic process ABCA for an ideal gas. a. What is the net energy transferred into the system by heat during each cycle? b. What would be the net energy transferred into the system by heat if the cycle followed the path ACBA instead? FIGURE P21.36 FIGURE P21.37arrow_forward
- A gas in a cylindrical closed container is adiabatically and quasi-statically expanded from a state A (3 MPa, 2 L) to a state B with volume of 6 L along the path 1.8pV= constant. (a) Plot the path in the pV plane. (b) Find the amount of work done by the gas and the change in the internal energy of the gas during the process.arrow_forwardFigure P22.73 illustrates the cycle ABCA for a 2.00-mol sample of an ideal diatomic gas, where the process CA is a reversible isothermal expansion. What is a. the net work done by the gas during one cycle? b. How much energy is added to the gas by heat during one cycle? c. How much energy is exhausted from the gas by heat during one cycle? d. What is the efficiency of the cycle? e. What would be the efficiency of a Carnot engine operated between the temperatures at points A and B during each cycle?arrow_forwardA sample of a monatomic ideal gas occupies 5.00 L at atmospheric pressure and 300 K (point A in Fig. P17.68). It is warmed at constant volume to 3.00 atm (point B). Then it is allowed to expand isothermally to 1.00 atm (point C) and at last compressed isobarically to its original state. (a) Find the number of moles in the sample. Find (b) the temperature at point B, (c) the temperature at point C, and (d) the volume at point C. (e) Now consider the processes A B, B C, and C A. Describe how to carry out each process experimentally. (f) Find Q, W, and Eint for each of the processes. (g) For the whole cycle A B C A, find Q, W, and Eint. Figure P17.68arrow_forward
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