Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 10, Problem 2P
To determine
The most probable speed of a gas molecule.
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You are studying a gas known as "gopherine" and looking in the literature you find that someone has
reported the partition function for one molecule of this gas,
5/2
AzT
q(V, T) = )
%3D
h?m
Assume that the molecules are independent and indistinguishable. Derive the expressions for the
energy, (E), for this gas. Give your answers in terms of N, kg, T. V and the constants A and B.
O (E) = NkaT
ㅇ (E) =D NkaT
ㅇ (E) %3D NkaT-
O (E) = ANKET -
O (E) = - T
ㅇ (E)=D 쑤-
Assume that air is an ideal gas under a uniform gravitational field, so that the potential energy of a molecule of mass m at altitude z is mgz. Show that the distribution of molecules varies with altitude as given by the distribution function f(z) dz = Cz exp(-βmgz) dz and that the normalization constant Cz= mg/kT. This distribution is referred to as the law of atmospheres.
Maxwell velocity distribution. Consider an ideal gas that obeys a Maxwell velocity distribution.
Each particle has mass m.
(a) Calculate the expected kinetic energy of a gas molecule using the Maxwell distribution.
Could you have calculated the expected value another way?
(b) Is your answer to part (a) equal to (i)mc² , (ii)mums , (ii) ;mup, none of these.
Recall C is the average speed,Urms is the root-mean-square speed, and Ump is the most
probable speed. Show your work.
(c) If the temperature is held constant, but the mass m of each particle is increased by
a factor of 4, by how much does your answer to (a) change? By how much does C
change?
Chapter 10 Solutions
Modern Physics
Ch. 10 - Prob. 1QCh. 10 - Prob. 2QCh. 10 - Prob. 1PCh. 10 - Prob. 2PCh. 10 - Prob. 3PCh. 10 - Prob. 4PCh. 10 - Prob. 5PCh. 10 - Prob. 6PCh. 10 - Prob. 8PCh. 10 - The light from a heated atomic gas is shifted in...
Ch. 10 - Prob. 10PCh. 10 - To obtain a more clearly defined picture of the...Ch. 10 - Prob. 12PCh. 10 - Prob. 14PCh. 10 - Prob. 15PCh. 10 - Prob. 16PCh. 10 - Prob. 17PCh. 10 - Prob. 18PCh. 10 - Prob. 19PCh. 10 - Prob. 20PCh. 10 - Prob. 21PCh. 10 - Prob. 22PCh. 10 - Prob. 23PCh. 10 - Prob. 24PCh. 10 - Prob. 26P
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