Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 16, Problem 46P
From the Maxwell–Boltzmann speed distribution, show that the most probable speed of a gas molecule is given by Equation 16.23. Note: The most probable speed corresponds to the point at which the slope of the speed distribution curve
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Only answer letters (d) and (e)
a) Using the Maxwell-Boltzmann function, calculate the fraction of argon gas molecules with a speed of 305 m/s at 500 K. (ans: 0.0014)
b) If the system in (a) has 0.46 moles of argon gas, how many molecules have the speed of 305 m/s? (ans: 6.44 x 10-4)
c) Calculate the values of vmp, vavg, and vrms for xenon gas at 298 K. (ans: Vmp=194.2 m/s , Vavg=219.2 m/s , Vrms=237.8 m/s)
d) From the values calculated in (c), label the Boltzmann distribution plot with the approximate locations of vmp, v avg, and vrms
e) What will have a larger speed distribution, helium at 500 K or argon at 300 K? Helium at 300 K or argon at 500 K? Argon at 400 K or argon at 1000 K?
A gas is cooled and trapped in a two-dimensional region by laser beams and magnets. The speed distribution function of the gas molecules obeys the two-dimensional Maxwell-Boltzmann distribution law,
f(v)=2π(m2πkB T)ve−mv22kB T
where m is the mass of a gas molecule, T is the temperature, and v is the speed. What is the average speed of the gas molecule?
Consider air at P = 1.00 atm. The average molecular mass of air is approximately 29 u. Boltzmann constant is 1.380 × 10−23 J/K.
What is the total translational kinetic energy of the gas molecules of air at atmospheric pressure that occupies a volume of 1.80 L (in J)?
Chapter 16 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 16.2 - Consider the following pairs of materials. Which...Ch. 16.3 - Prob. 16.2QQCh. 16.4 - A common material for cushioning objects in...Ch. 16.4 - Prob. 16.4QQCh. 16.5 - Two containers hold an ideal gas at the same...Ch. 16.6 - Prob. 16.6QQCh. 16 - Prob. 1OQCh. 16 - A cylinder with a piston holds 0.50 m3 of oxygen...Ch. 16 - A hole is drilled in a metal plate. When the metal...Ch. 16 - When a certain gas under a pressure of 5.00 106...
Ch. 16 - Prob. 5OQCh. 16 - Prob. 6OQCh. 16 - What would happen if the glass of a thermometer...Ch. 16 - Prob. 8OQCh. 16 - A gas is at 200 K. If we wish to double the rms...Ch. 16 - Prob. 10OQCh. 16 - Prob. 11OQCh. 16 - A rubber balloon is filled with 1 L of air at 1...Ch. 16 - Prob. 13OQCh. 16 - An ideal gas is contained in a vessel at 300 K....Ch. 16 - Prob. 15OQCh. 16 - Prob. 16OQCh. 16 - Prob. 17OQCh. 16 - A sample of gas with a thermometer immersed in the...Ch. 16 - Prob. 19OQCh. 16 - Prob. 1CQCh. 16 - Prob. 2CQCh. 16 - Prob. 3CQCh. 16 - A piece of copper is dropped into a beaker of...Ch. 16 - Prob. 5CQCh. 16 - Prob. 6CQCh. 16 - Prob. 7CQCh. 16 - Prob. 8CQCh. 16 - Prob. 9CQCh. 16 - Prob. 10CQCh. 16 - Prob. 11CQCh. 16 - Prob. 12CQCh. 16 - Prob. 13CQCh. 16 - Prob. 1PCh. 16 - Convert the following to equivalent temperatures...Ch. 16 - Prob. 3PCh. 16 - Prob. 4PCh. 16 - Prob. 5PCh. 16 - Prob. 6PCh. 16 - Prob. 7PCh. 16 - Prob. 8PCh. 16 - Prob. 9PCh. 16 - A sample of a solid substance has a mass m and a...Ch. 16 - Each year thousands of children are badly burned...Ch. 16 - Prob. 12PCh. 16 - Prob. 13PCh. 16 - Prob. 14PCh. 16 - The active element of a certain laser is made of a...Ch. 16 - Prob. 16PCh. 16 - Prob. 17PCh. 16 - Prob. 18PCh. 16 - Prob. 19PCh. 16 - Prob. 20PCh. 16 - Prob. 21PCh. 16 - Prob. 22PCh. 16 - Prob. 23PCh. 16 - Prob. 24PCh. 16 - Prob. 25PCh. 16 - Prob. 26PCh. 16 - Prob. 27PCh. 16 - Prob. 28PCh. 16 - The mass of a hot-air balloon and its cargo (not...Ch. 16 - Prob. 30PCh. 16 - A popular brand of cola contains 6.50 g of carbon...Ch. 16 - Prob. 32PCh. 16 - At 25.0 m below the surface of the sea, where the...Ch. 16 - To measure how far below the ocean surface a bird...Ch. 16 - Prob. 35PCh. 16 - Prob. 36PCh. 16 - Prob. 37PCh. 16 - Prob. 38PCh. 16 - Prob. 39PCh. 16 - A cylinder contains a mixture of helium and argon...Ch. 16 - Prob. 41PCh. 16 - Prob. 42PCh. 16 - Prob. 43PCh. 16 - (a) How many atoms of helium gas fill a spherical...Ch. 16 - Fifteen identical particles have various speeds:...Ch. 16 - From the MaxwellBoltzmann speed distribution, show...Ch. 16 - Prob. 47PCh. 16 - Helium gas is in thermal equilibrium with liquid...Ch. 16 - Prob. 49PCh. 16 - Prob. 50PCh. 16 - Prob. 51PCh. 16 - Prob. 52PCh. 16 - A mercury thermometer is constructed as shown in...Ch. 16 - A liquid with a coefficient of volume expansion ...Ch. 16 - A clock with a brass pendulum has a period of...Ch. 16 - A vertical cylinder of cross-sectional area A is...Ch. 16 - Prob. 57PCh. 16 - Prob. 58PCh. 16 - Prob. 59PCh. 16 - The rectangular plate shown in Figure P16.60 has...Ch. 16 - In a chemical processing plant, a reaction chamber...Ch. 16 - Prob. 62PCh. 16 - Prob. 63PCh. 16 - Two concrete spans that form a bridge of length L...Ch. 16 - A 1.00-km steel railroad rail is fastened securely...Ch. 16 - Prob. 66PCh. 16 - Prob. 67PCh. 16 - Prob. 68PCh. 16 - Consider an object with any one of the shapes...Ch. 16 - Prob. 70PCh. 16 - Prob. 71PCh. 16 - Prob. 72PCh. 16 - Prob. 73PCh. 16 - A cylinder that has a 40.0-cm radius and is 50.0...Ch. 16 - Prob. 75P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- Give the temperature T of 1 mole of ideal gas as a function of the pressure P, volume V, and the gas constant R and give the internal energy U of a rigid diatomic ideal gas as a function of its temperature T and the gas constant R.arrow_forwardWhat would the pressure ? of an ideal gas be if the mean free path was 1.30×102 cm? Assume that the gas is at room temperature, ?=20.0 ∘C, and that the diameter of the molecule is ?=3.00×10−10 m.arrow_forwardThe density of air at standard conditions (P = 1 atm and T = 20oC) is 1.28 kg/m3. At what pressure is the density 0.64 kg/m3 if the temperature and number of molecules are kept constant?arrow_forward
- Find the molar mass and the number of degrees of freedom of molecules in a gas if cV=0.65J/gK and cP=0.91J/g K.arrow_forwardWhat, 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_forwardA sample of 3 mol of diatomic gas is measured to have a temperature of 300 K. If the mass of the gas is 0.048 kg, what is the approximate average speed of the molecules in the gas ? (Recall that the equation for kinetic energy due to translation in a gas is and R=8.31 J/(mol K). KE translational = 1 2 mv^ 2 = 3 2 nRT, A. 612 m/s B. 684 m/s C. 670 m/s D. 608 m/sarrow_forward
- Pretend that you live in the 19th century and don't know the value of Avogadro's number* (or of Boltzmann's constant or of the mass or size of any molecule). Show how you could make a rough estimate of Avogadro's number from a measurement of the thermal conductivity of a gas, together with other measurements that are relatively easy.arrow_forwardThe partial pressure of carbon dioxide in the lungs is about 470 Pa when the total pressure in the lungs is 1.0 atm. What percentage of the air molecules in the lungs is carbon dioxide? Compare your result to the percentage of carbondioxide in the atmosphere, about 0.033%.arrow_forwardA cylinder contains 0.020 m3 of molecular oxygen at a temperature of 25 C and a pressure of 15 atm. What would be the volume of this gas at a pressure of an atmosphere? A patient breathes this oxygene using a mask has a rate 0.0080 m3/minute at atmospheric pressure. After how long will the cylinder be 'empty' i.e. its pressure will be 1 atm.arrow_forward
- Consider 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_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_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
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
The Laws of Thermodynamics, Entropy, and Gibbs Free Energy; Author: Professor Dave Explains;https://www.youtube.com/watch?v=8N1BxHgsoOw;License: Standard YouTube License, CC-BY