Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
12th Edition
ISBN: 9781259587399
Author: Eugene Hecht
Publisher: McGraw-Hill Education
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Chapter 17, Problem 23SP
To determine
The kinetic energy of 1.00 mole of any gas at the temperature of
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A 7.00-L vessel contains 3.50 moles of ideal gas at a pressure of 1.60 x 106 Pa. Find (a) the temperature of the gas and (b) the average kinetic energy of a gas molecule in the vessel. (c) What additional information would you need if you were asked to find the average speed of a gas molecule?
A flexible, sealed balloon contains an ideal gas initially at room temperature (293 K). If the balloon is gently heated to 330 K and the gas maintains a constant pressure, what
happens to the volume and total random translational kinetic energy of the gas?
Both the volume and total kinetic energy increase.
The volume increases while the total kinetic energy decreases.
Both the volume and total kinetic energy remain constant.
The volume decreases while the total kinetic energy increases.
Both the volume and total kinetic energy decrease.
Equal moles of three different ideal gases (A, B, and C) are prepared in separate sealed
chambers at different temperatures. The velocity distributions for molecules of the three
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Which of the following statements about these gases MUST BE true?
Number of Molecules
B
C
Velocity
Gas C has the greatest temperature.
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O Gas A has the greatest molecular mass.
O Gas C has the greatest rms speed.
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Chapter 17 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
Ch. 17 - Prob. 13SPCh. 17 - 17.14 [II] A typical polymer molecule in...Ch. 17 - 17.15 [II] A certain strain of tobacco mosaic...Ch. 17 - 17.16 [I] If the Celsius temperature of a gas...Ch. 17 - 17.17 [I] What happens to the average kinetic...Ch. 17 - 17.18 [I] The absolute temperature of a sample of...Ch. 17 - Prob. 19SPCh. 17 - Prob. 21SPCh. 17 - Prob. 22SPCh. 17 - Prob. 23SP
Ch. 17 - Prob. 24SPCh. 17 - Prob. 25SPCh. 17 - Prob. 26SPCh. 17 - Prob. 27SPCh. 17 - Prob. 28SPCh. 17 - 17.29 [II] In a certain region of outer space...Ch. 17 - 17.30 [II] A cube of aluminum has a volume of 1.0 ...Ch. 17 - 17.31 [II] The rms speed of nitrogen molecules in...Ch. 17 - 17.32 [II] What is the mean free path of a gas...
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- Find (a) the most probable speed, (b) the average speed, and (c) the rms speed for nitrogen molecules at 295 K.arrow_forwardConsider a gas filling two connected chambers that are separated by a removable barrier (Fig. P20.68). The gas molecules on the left (red) are initially at a higher temperature than the ones on the right (blue). When the barrier between the two chambers is removed, the molecules begin to mix and move from one chamber to the other. a. Describe what happens to the temperature in the left chamber and in the right chamber as time goes on, once the barrier is open. Discuss in terms of the mixing of the molecules from each gas. b. Describe what happens to the most probable speed and average speed in the left chamber and in the right chamber as time goes on, once the barrier is open. Do they increase or decrease by the same factor? Explain. FIGURE P20.68 Problems 68 and 69.arrow_forwardA 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_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 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_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
- 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_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_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
- An ideal gas is contained in a vessel at 300 K. The temperature of the gas is then increased to 900 K. (i) By what factor does the average kinetic energy of the molecules change, (a) a factor of 9, (b) a factor of 3, (c) a factor of 3, (d) a factor of 1, or (e) a factor of 13? Using the same choices as in part (i), by what factor does each of the following change: (ii) the rms molecular speed of the molecules, (iii) the average momentum change that one molecule undergoes in a collision with one particular wall, (iv) the rate of collisions of molecules with walls, and (v) the pressure of the gas?arrow_forwardEvaluate rms speed, the average kinetic energy of a molecule and total random kinetic energy of all the molecules in 6 moles of air gas at a temperature of 700 K. (Molar mass of air is 28.97 x 10-3 mole/kg, and kB = 1.38 x 10-23 J/K)arrow_forwardWhat is the average translational kinetic energy of an ideal-gas molecule at 27 C? (b) What is the total random translational kinetic energy of the molecules in 1 mole of this gas? (c) What is the rms speed of oxygen molecules at this temperature?arrow_forward
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