A box of 10.0 cm x 10.0 cm x 10.0 cm contains 12 x 105 Pa of N2 gas molecules at25°C. The mass of one N₂ molecule is 4.68 x 1026 kg and its molar mass is 28.0-gAssume all the molecules collide with the container walls with its rms speed in ahead-on fashion and all the collisions are perfectly elastic, estimate the amount ofmolecules striking one side of the container wall in 10 seconds?(R = 8.31 J/mole/K = 0.08205 Latm/mole/K, kg-1.38 X 10 23 J/K, 1 atm = 1.01X10 5 Pa.)4.1 x 10282.9 x 10263.2 x 10207.5 x 10221.0 x 1024

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Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter20: Kinetic Theory Of Gases

Section: Chapter Questions

Problem 61PQ

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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.
How many moles are there in (a) 0.0500 g of N2 gas (M = 28.0 g/mol)? (b) 10.0 g of CO2 gas (M = 44.0 g/mol)? (c) How many molecules are present in each case?
Two monatomic ideal gases A and B are at the same temperature. If 1.0 g of gas A has the same internal energy as 0.10 g of gas B, what are (a) the ratio of the number of moles of each gas and (b) the ration of the atomic masses of the two gases?
From the MaxwellBoltzmann 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 dNv/dv is zero.
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.
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 P20.29ANS
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In interstellar space it is estimated that atomic hydrogen exists at a concentration of one particle per cubic meter. If the collision diameter is 2.5 x 1010 m, calculate the mean free path 2. The temperature of interstellar space is 2.7 K. 2.
By considering momentum changes for an individual molecule inside a rectangular box, derive an expression for PV in terms of molecular mass, the number of molecules, and mean square speed. Compare this to the ideal gas equation to show that the mean kinetic energy of a molecule is 1.5 kB
1- a) Consider a physical system composed of N identical particles confined to a space of volume V. Write the thermodynamic limit for this system. b) Write condition of ideal gas for real gas. c) Prove B =, where The universal constant k is generally referred to as the Boltzmann constant. d) For a physical system composed of N identical particles at temperatureOand confined to a space of volume V, prove the ideal gas low PV = NkT
A box of 10.0 cm x 10.0 cm x 10.0 cm contains 1.2 x 105 Pa of N2 gas molecules at 25°C. The mass of one N2 molecule is 4.68 x 10-26 kg and its molar mass is 28.0-g Assume all the molecules collide with the container walls with its rms speed in a head-on fashion and all the collisions are perfectly elastic, estimate the amount of molecules striking one side of the container wall in 10 seconds? (R = 8.31 J/mole/K -0.08205 Latm/mole/K, kg-1.38 X 10 23 J/K, 1 atm = 1.01X 105 Pa.) 4.1 x 1028 2.9 x 1026 3.2 x 1020 7.5 x 1022 10 x 1024 A Question 21 (4 points) Retake question I used equations in the list to solve the above problem: AT P = k₁A₁AT¹ + k2A22 + k3A3 P = KAAT AT3 L3 P = E/t P = AAT +AT+ A 1. Yes. 2. No. P=A- AT R₁+Ra+R3
The mean free path λ and the mean collision time T of molecules of a diatomic gas with molecular mass 6.00 x10^-25 kg and radius r=1.0x10^-10m are measured.From these microscopic data we can obtain macroscopic properties such as temperature T and pressure P? If yes, consider λ=4.32x10^-8m and T=3.00x10^-10s and calculate T and P.a)It's not possible.b)Yes,T=150K and P~2.04atm.c)Yes,T=150K and P~4.08atm.d)Yes,T=300K and P~4.08atm.e)Yes,T=300K and P~5.32atmf)Yes,T=400K and P~4.08atmg)Yes,T=400K and P~5.32atm.

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