Physics for Scientists and Engineers
10th Edition
ISBN: 9781337553278
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 20, Problem 31AP
The Earth’s atmosphere consists primarily of oxygen (21%) 30 and nitrogen (78%). The rms speed of oxygen molecules (O2) in the atmosphere at a certain location is 535 m/s. (a) What is the temperature of the atmosphere at this location? (b) Would the rms speed of nitrogen molecules (N2) at this location be higher, equal to, or lower than 535 m/s? Explain. (c) Determine the rms speed of N2 at his location.
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At what temperature does the rms speed of (a) H2 (molecular hydrogen) and (b) O2 (molecular oxygen) equal the escape speed from Earth? At what temperature does the rms speed of (c) H2 and (d) O2 equal the escape speed from the Moon (where the gravitational acceleration at the surface has magnitude 0.16g)? Considering the answers to parts (a) and (b), should there be much (e) hydrogen and (f) oxygen high in Earth’s upper atmosphere, where the temperature is about 1000 K?
Chapter 20 Solutions
Physics for Scientists and Engineers
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 - Oxygen, modeled as an ideal gas, is in a container...Ch. 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 - A 1.00-L insulated bottle is full of tea at 90.0C....Ch. 20 - A certain molecule has f degrees of freedom. Show...Ch. 20 - You are working for an automobile tire company....Ch. 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 - Why is the following situation impossible? A new...Ch. 20 - Air (a diatomic ideal gas) at 27.0C and...Ch. 20 - Prob. 22PCh. 20 - Prob. 23PCh. 20 - Prob. 24PCh. 20 - Prob. 25PCh. 20 - The law of atmospheres states that the number...Ch. 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 - Review. As a sound wave passes through a gas, the...Ch. 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 - A sample consists of an amount n in moles of a...Ch. 20 - The latent heat of vaporization for water at room...Ch. 20 - A vessel contains 1.00 104 oxygen molecules at...Ch. 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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- Cylinder A contains oxygen (O2) gas, and cylinder B contains nitrogen (N2) gas. If the molecules in the two cylinders have the same rms speeds, which of the following statements is false? (a) The two gases haw different temperatures. (b) The temperature of cylinder B is less than the temperature of cylinder A. (c) The temperature of cylinder B is greater than the temperature of cylinder A. (d) The average kinetic energy of the nitrogen molecules is less than the average kinetic energy of the oxygen molecules.arrow_forwardConsider the Maxwell-Boltzmann distribution function plotted in Problem 28. For those parameters, determine the rms velocity and the most probable speed, as well as the values of f(v) for each of these values. Compare these values with the graph in Problem 28. 28. Plot the Maxwell-Boltzmann distribution function for a gas composed of nitrogen molecules (N2) at a temperature of 295 K. Identify the points on the curve that have a value of half the maximum value. Estimate these speeds, which represent the range of speeds most of the molecules are likely to have. The mass of a nitrogen molecule is 4.68 1026 kg. Equation 20.18 can be used to find the rms velocity given the temperature, Boltzmanns constant, and the mass of the atom or molecule. The mass of a nitrogen molecule is 4.68 1026 kg. vrms=3kBTm=3(1.381023J/K)4.681026kg=511m/s Using the results of Problem 28 and the rms velocity, we can calculate the value of f(v). f(vrms) = (3.11 108)(511)2 e(5.75106(511)2) = 0.00181 The most probable speed, for which this function has its maximum value, is given by Equation 20.20. vmp=2kBTm=2(1.381023J/K)(295K)4.681026kg=417m/s f(vmp) = (3.11108)(417)2 e(5.75106(417)2) = 0.00199 We plot these points on the speed distribution. The most probable speed is indeed at the peak of the distribution function. Since the function is not symmetric, the rms velocity is somewhat higher than the most probable speed. Figure P20.29ANSarrow_forwardOne cylinder contains helium gas and another contains krypton gas at the same temperature. Mark each of these statements true, false, or impossible to determine from the given information. (a) The rms speeds of atoms in the two gases are the same. (b) The average kinetic energies of atoms in the two gases are the same. (c) The internal energies of 1 mole of gas in each cylinder are the same. (d) The pressures in the two cylinders ale the same.arrow_forward
- Fifteen identical particles have various speeds: one has a speed of 2.00 m/s, two have speeds of 3.00 m/s, three have speeds of 5.00 m/s, four have speeds of 7.00 m/s, three have speeds of 9.00 m/s, and two have speeds of 12.0 m/s. Find (a) the average speed, (b) the rms speed, and (c) the most probable speed of these particles.arrow_forwardA gas is at 200 K. If we wish to double the rms speed of the molecules of the gas, to what value must we raise its temperature? (a) 283 K (b) 400 K (c) 566 K (d) 800 K (e) 1 130 Karrow_forwardOn a hot summer day, the density of air at atmospheric pressure at 35.0C is 1.1455 kg/m3. a. What is the number of moles contained in 1.00 m3 of an ideal gas at this temperature and pressure? b. Avogadros number of air molecules has a mass of 2.85 102 kg. What is the mass of 1.00 m3 of air? c. Does the value calculated in part (b) agree with the stated density of air at this temperature?arrow_forward
- Two containers hold an ideal gas at the same temperature and pressure. Both containers hold the same type of gas, but container B has twice the volume of container A. (i) What is the average translational kinetic energy per molecule in container B? (a) twice that of container A (b) the same as that of container A (c) half that of container A (d) impossible to determine (ii) From the same choices, describe the internal energy of the gas in container B.arrow_forwardA sample of a monatomic ideal gas occupies 5.00 L at atmospheric pressure and 300 K (point A in Fig. P21.65). 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.arrow_forward
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