Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 20, Problem 24P
To determine
To show: The most probable speed of a gas molecule is given by
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S 3
The free energy is defined as follows:
av (k₂1)³2
5/2
F = Nk, Tin
N
Here, Nis the number of particles of gas, Vis the volume of the gas, I is the
k₂
temperature of the gas, is the Boltzmann constant, and is the constant.
What is the internal energy of the gas?
(a) - NKT
(b)-NK, I
(c) Nk T
(d) ——— Nk¸T
Calculate the average speed, ī of molecules in a gas using the Maxwell-Boltzmann distribution function.
You will need the following Gaussian integral relation,
1
ve-au du
%3D
2a²
Chapter 20 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 20.1 - Two containers hold an ideal gas at the same...Ch. 20.2 - (i) How does the internal energy of an ideal gas...Ch. 20.3 - Prob. 20.3QQCh. 20.3 - Prob. 20.4QQCh. 20 - A spherical balloon of volume 4.00 103 cm3...Ch. 20 - A spherical balloon of volume V contains helium at...Ch. 20 - A 2.00-mol sample of oxygen gas is confined to a...Ch. 20 - Prob. 4PCh. 20 - A 5.00-L vessel contains nitrogen gas at 27.0C and...Ch. 20 - Prob. 6P
Ch. 20 - In a period of 1.00 s, 5.00 1023 nitrogen...Ch. 20 - A 7.00-L vessel contains 3.50 moles of gas at a...Ch. 20 - Calculate the change in internal energy of 3.00...Ch. 20 - Prob. 10PCh. 20 - In a constant-volume process, 209 J of energy is...Ch. 20 - A vertical cylinder with a heavy piston contains...Ch. 20 - Prob. 13PCh. 20 - A certain molecule has f degrees of freedom. Show...Ch. 20 - Prob. 15PCh. 20 - Why is the following situation impossible? A team...Ch. 20 - You and your younger brother are designing an air...Ch. 20 - During the compression stroke of a certain...Ch. 20 - Air in a thundercloud expands as it rises. If its...Ch. 20 - Prob. 20PCh. 20 - Air (a diatomic ideal gas) at 27.0C and...Ch. 20 - Prob. 22PCh. 20 - Prob. 23PCh. 20 - Prob. 24PCh. 20 - Prob. 25PCh. 20 - Prob. 26PCh. 20 - Prob. 27APCh. 20 - Prob. 28APCh. 20 - The dimensions of a classroom are 4.20 m 3.00 m ...Ch. 20 - Prob. 30APCh. 20 - The Earths atmosphere consists primarily of oxygen...Ch. 20 - Prob. 32APCh. 20 - Prob. 33APCh. 20 - In a cylinder, a sample of an ideal gas with...Ch. 20 - As a 1.00-mol sample of a monatomic ideal gas...Ch. 20 - Prob. 36APCh. 20 - Prob. 37APCh. 20 - Prob. 38APCh. 20 - Prob. 39APCh. 20 - Prob. 40APCh. 20 - Prob. 41APCh. 20 - On the PV diagram for an ideal gas, one isothermal...Ch. 20 - Prob. 43APCh. 20 - Prob. 44APCh. 20 - Prob. 45CP
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- 1. From the Maxwell-Boltzmann speed distribution, show that the most probable speed of a gas molecule is given by: Vmp = 2 KBT m Note: The most probable speed corresponds to the point at which the slope of the speed distribution curve dNv/dv is zero.arrow_forwardAt what temperature would the rms speed of helium atoms equal a. the escape speed from Earth, 1.12 m/s b. the escape speed from the Moon, 2.37 m/s? Note: The mass of a helium atom is 6.64 x 10-27 kg and the Boltzmann’s constant isarrow_forwardHow to use Boltzmann factors to derive the exponential formula for the density of an isothermal atmosphere. (Hint: Let the system be a single air molecule, let 81 be a state with the molecule at sea level, and let 82 be a state with the molecule at height z)arrow_forward
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