Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 22, Problem 54PQ
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For an ideal gas enclosed in a container at temperature T, by using Maxwell’s speed distribution law, derive the expressions for rms speed and most probable speed of its molecules.
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Chapter 22 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 22.2 - Prob. 22.1CECh. 22.4 - Prob. 22.2CECh. 22.5 - Prob. 22.3CECh. 22.7 - You have considerable intuition about whether some...Ch. 22.9 - Prob. 22.5CECh. 22 - Prob. 1PQCh. 22 - Heat Engines Figure P22.2 shows a Carnot cycle....Ch. 22 - Use a PV diagram such as the one in Figure 22.2...Ch. 22 - Prob. 4PQCh. 22 - Prob. 5PQ
Ch. 22 - Prob. 6PQCh. 22 - An engine with an efficiency of 0.36 can supply a...Ch. 22 - Prob. 8PQCh. 22 - Prob. 9PQCh. 22 - Prob. 10PQCh. 22 - Prob. 11PQCh. 22 - Prob. 12PQCh. 22 - Prob. 13PQCh. 22 - Prob. 14PQCh. 22 - Prob. 15PQCh. 22 - Prob. 16PQCh. 22 - Prob. 17PQCh. 22 - Prob. 18PQCh. 22 - Prob. 19PQCh. 22 - Prob. 20PQCh. 22 - Prob. 21PQCh. 22 - In 1816, Robert Stirling, a Scottish minister,...Ch. 22 - Prob. 23PQCh. 22 - Prob. 24PQCh. 22 - Prob. 25PQCh. 22 - Prob. 26PQCh. 22 - Prob. 27PQCh. 22 - Prob. 28PQCh. 22 - Prob. 29PQCh. 22 - Prob. 30PQCh. 22 - Prob. 31PQCh. 22 - Prob. 32PQCh. 22 - Prob. 33PQCh. 22 - Prob. 34PQCh. 22 - Prob. 35PQCh. 22 - Estimate the change in entropy of the Universe if...Ch. 22 - Prob. 37PQCh. 22 - Prob. 38PQCh. 22 - Prob. 39PQCh. 22 - Prob. 40PQCh. 22 - Prob. 41PQCh. 22 - Prob. 42PQCh. 22 - Prob. 43PQCh. 22 - Prob. 44PQCh. 22 - Prob. 45PQCh. 22 - Prob. 46PQCh. 22 - Prob. 47PQCh. 22 - Prob. 48PQCh. 22 - Prob. 49PQCh. 22 - Prob. 50PQCh. 22 - Prob. 51PQCh. 22 - Prob. 52PQCh. 22 - Prob. 53PQCh. 22 - Prob. 54PQCh. 22 - Prob. 55PQCh. 22 - Prob. 56PQCh. 22 - What is the entropy of a freshly shuffled deck of...Ch. 22 - Prob. 58PQCh. 22 - Prob. 59PQCh. 22 - Prob. 60PQCh. 22 - Prob. 61PQCh. 22 - Prob. 62PQCh. 22 - Prob. 63PQCh. 22 - Prob. 64PQCh. 22 - Prob. 65PQCh. 22 - Prob. 66PQCh. 22 - Prob. 67PQCh. 22 - Prob. 68PQCh. 22 - Prob. 69PQCh. 22 - Prob. 70PQCh. 22 - A system consisting of 10.0 g of water at a...Ch. 22 - Prob. 72PQCh. 22 - Figure P22.73 illustrates the cycle ABCA for a...Ch. 22 - Prob. 74PQCh. 22 - Prob. 75PQCh. 22 - Prob. 76PQCh. 22 - Prob. 77PQCh. 22 - Prob. 78PQCh. 22 - Prob. 79PQCh. 22 - Prob. 80PQCh. 22 - Prob. 81PQ
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- How many molecules are in a typical object, such as gas in a tire or water in a drink? We can use the ideal gas law to give us an idea of how large N typically is.Calculate the number of molecules in a cubic meter of gas at standard temperature and pressure (STP), which is defined to be 0ºC and atmospheric pressure.arrow_forwardBy 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 kBarrow_forwardConsider the ideal gas H2 at T = 293 K. Use a numerical integration program on a computer to find the fraction of molecules with speeds in the following ranges: (a) 0 to 10 m/s, (b) 0 to 100 m/s, (c) 0 to 1000 m/s, (d) 1000 m/s to 2000 m/s, (e) 2000 m/s to 5000 m/s, and (f) 0 to 5000 m/s.arrow_forward
- Helparrow_forwardA gaseous system A, with an initial temperature T1, is set to interact with a gaseous system B at an initial temperature T2. The molecules of A and B, both monoatomic, can interact with each other through a wall without mixing. It is known that T2 > T1. Considering this situation, answer the following question. Consider the statements below and type the sum of the numbers associated with the correct ones (write only the number): (1) After thermal equilibrium is reached, the system with more molecules necessarily has the higher energy (2) Equilibrium occurs when the energy of A is equal to that of B (4) At equilibrium, the average kinetic energy per molecule is the same in both systems (8) At equilibrium, molecules with greater mass will have, on average, a greater kinetic energy (16) At equilibrium, more massive molecules will, on average, be slower than lighter moleculesarrow_forwardThe 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.arrow_forward
- Real gases For helium gas, the critical temperature is Tk=5.2K and the critical pressure is Pk=0.23x10^6 Pa. Assuming that the helium gas obeys the Van der Waals equation, calculate the Van der Waals constants a and b, and the density of helium in the critical state.arrow_forwarda) Find the difference of molar-specific heats Cp - C, for the gas covered by the equation of state: (P+) (V - b) = RT b) Determine the volume of the hypersphere in N-dimensional space. c) An ideal gas consists of N monatomic molecules. Using the grand canonical ensemble, (T-μ) distribution, calculate the chemical potential, pressure, and entropy.arrow_forwardConsider a case of n particles and two compartments, if n1 is the number of particles in one compartment and remaining n2=n-n1 particles in other compartment, then the number of microstates in the macrostate (n1, n-n1) or thermodynamic probability isarrow_forward
- A)An ideal gas is confined to a container at a temperature of 330 K.What is the average kinetic energy of an atom of the gas? (Express your answer to two significant figures.) B)2.00 mol of the helium is confined to a 2.00-L container at a pressure of 11.0 atm. The atomic mass of helium is 4.00 u, and the conversion between u and kg is 1 u = 1.661 ××10−27 kg.Calculate vrmsvrms. (Express your answer to three significant figures.) C)A gold (coefficient of linear expansion α=14×10−6K−1α=14×10−6K−1 ) pin is exactly 4.00 cm long when its temperature is 180∘∘C. Find the decrease in long of the pin when it cools to 28.0∘∘C? (Express your answer to two significant figures.)arrow_forwardConsider a one-dimensional gas consisting of N = 5 particles each of which has the same speed v, but can move in one of two directions with equal probability. The velocity of each particle is independent. What is the probability that all particles are moving in the same direction?arrow_forwardConsider a container filled with helium gas at room temperature and ambient pressure. (a) Sketch a graph of the distribution of molecular speeds in the container. (b) On the same graph, sketch the distribution for the same container at a lower temperature, clearly labelling the new curve.arrow_forward
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