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 2CQ
To determine
Does diatomic gas have greater energy content than an monatomic gas at same temperature.
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The only form of energy possessed by molecules of a monatomic ideal gas is translational kinetic energy. From kinetic, the average kinetic energy per molecule is
KEmolecule =
3
2
kBT =
3
2
R
NA
T
Use these results to show that the internal energy of a monatomic ideal gas at pressure P and occupying volume V may be written as
U =
3
2
PV.
The temperature of 2.85 mol of an ideal diatomic gas is increased by 51.3 °C without the pressure of the gas changing. The molecules in
the gas rotate but do not oscillate. (a) How much energy is transferred to the gas as heat? (b) What is the change in the internal energy
of the gas? (c) How much work is done by the gas? (d) By how much does the rotational kinetic energy of the gas increase?
(a) Number
i
Units
(b) Number
Units
Units
(c) Number
Units
(d) Number
One might think that the internal energy of diatomic gases is given by Eint = 5RT/2. Do diatomic gases near room temperature have more or less internal energy than that? Hint: Their internal energy includes the total energy added in raising the temperature from the boiling point (very low) to room 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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- 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_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_forwardTwo 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_forward
- A 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_forwardFor a temperature increase of 10 at constant volume, what is the heat absorbed by (a) 3.0 mol of a dilute monatomic gas; (b) 0.50 mol of a dilute diatomic gas; and (c) 15 mol of a dilute polyatomic gas?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_forward
- A 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_forwardAn ideal gas has a pressure of 0.50 atm and a volume of 10 L. It is compressed adiabatically and quasi-statically until its pressure is 3.0 atm and its volume is 2.8 L. Is the monatomic, diatomic, or polyatomic?arrow_forwardTwo moles of a monatomic ideal gas such as helium is compressed adiabatically and reversibly from a state (3 atm, 5 L) to a state with pressure 4 atm. (a) Find the volume and temperature of the final state. (b) Find the temperature of the initial state of the gas. (c) Find the work done by the gas in the process. (d) Find the change in internal energy of the gas in the process.arrow_forward
- What is the average mechanical energy of the atoms of an ideal monatomic gas at 300 K?arrow_forwardFind (a) the most probable speed, (b) the average speed, and (c) the rms speed for nitrogen molecules at 295 K.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_forward
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