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Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
9th Edition
ISBN: 9781305932302
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 21, Problem 42P
To determine
Show that the most probable speed of a gas molecule is given by the equation 21.44.
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Students have asked these similar questions
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
A cylinder of diameter S, of height h, contains pure gas with equation
PV = nRT at constant temperature T_0. The z axis is directed upwards
and the gravitational field is assumed to be uniform.
1) Using the fundamental principle of hydrostatic statistics, show that
dp = -pgdz where p = p (z) is the gas pressure at height z.
2) If P_0 is the gas pressure at the foot of the pole, calculate the
pressure p (z) at height z.
3) In the case of wind (M = 29 g / mol: R = 8.31J/ mol.k) at
temperature T_0 = 300K, calculate the height of the poles necessary
to observe the change in pressure (pressure at the threshold) at 5% .
Problem 6: There are lots of examples of ideal gases in the universe, and they exist in many different conditions. In this problem we will examine what the temperature of these various phenomena are.
Part (a) Give an expression for the temperature of an ideal gas in terms of pressure P, particle density per unit volume ρ, and fundamental constants.
T = P/( ρ kB )
Part (b) Near the surface of Venus, its atmosphere has a pressure fv= 96 times the pressure of Earth's atmosphere, and a particle density of around ρv = 0.92 × 1027 m-3. What is the temperature of Venus' atmosphere (in C) near the surface?
Part (c) The Orion nebula is one of the brightest diffuse nebulae in the sky (look for it in the winter, just below the three bright stars in Orion's belt). It is a very complicated mess of gas, dust, young star systems, and brown dwarfs, but let's estimate its temperature if we assume it is a uniform ideal gas. Assume it is a sphere of radius r = 5.8 × 1015 m (around 6 light years)…
Chapter 21 Solutions
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
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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- What, according to the Maxwell–Boltzmann distribution, is the proportion of gas molecules having (i) more than, (ii) less than the root mean square speed? (iii) What are the proportions having speeds greater and smaller than the mean speed?arrow_forwardCalculate 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 2a²arrow_forwardYou 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-arrow_forward
- 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_forwardAn expensive vacuum system can achieve a pressure as low as 1.00 x 10-7 N/m² at 25.5 °C. How many atoms N are there in a cubic centimeter at this pressure and temperature? The Boltzmann constant k = 1.38 x 10-23 J/K. N = atomsarrow_forwardThese two questions relate to the Boltzmann Equation. A gas of neutral hydrogen atoms in local thermodynamical equilibrium has 1/3 more atoms in the energy level n = 1 than in the n = 2 state. Calculate the temperature of that gas. For a gas of neutral hydrogen atoms make a graph that shows the ratios N2/N1, N3/N1, N4/N1 as a function of T.arrow_forward
- At 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_forwardWhat is the mean free path of molecules in an ideal gas in which the mean collision time is 4.00 × 10-10 s, the temperature is 294K, and the mass of the molecules is 6.00 × 10-25 kg? Assume that the molecules are moving at their root-mean-square speeds. The Boltzmann constant is 1.38 × 10-23 J/K. GIve your answer in Angstroms ( 1 Angstrom = 10-10 m)arrow_forwardRedlich-Kwong equation of state for real gas is P=[RT/(V-b)]-[a/V(V+b)T0.5]. Show that the value of constant a is: a=0.427(R2Tc5/2)/Pcarrow_forward
- How 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_forwardHow does the Boltzmann distribution and statistics explain the behavior of an ideal gas in terms of the distribution of molecular energies and the probability of various energy states?arrow_forwardPlease answer all parts: Problem 3: There are lots of examples of ideal gases in the universe, and they exist in many different conditions. In this problem we will examine what the temperature of these various phenomena are. Part (a) Give an expression for the temperature of an ideal gas in terms of pressure P, particle density per unit volume ρ, and fundamental constants. T = ______ Part (b) Near the surface of Venus, its atmosphere has a pressure fv= 91 times the pressure of Earth's atmosphere, and a particle density of around ρv = 0.91 × 1027 m-3. What is the temperature of Venus' atmosphere (in C) near the surface? Part (c) The Orion nebula is one of the brightest diffuse nebulae in the sky (look for it in the winter, just below the three bright stars in Orion's belt). It is a very complicated mess of gas, dust, young star systems, and brown dwarfs, but let's estimate its temperature if we assume it is a uniform ideal gas. Assume it is a sphere of radius r = 5.7 × 1015 m…arrow_forward
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