Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 17, Problem 14P
To determine
The average speed of the molecule when the absolute temperature of the gas doubles.
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What macroscopic property of an ideal gas doubles when the absolute temperature is doubled while keeping the pressure constant?
If you cool an ideal gas, such that the the absolute temperature of gas is reduced by half, then theaverage speed of the molecules that make up the gas will change by what factor?
A gas is contained in a rigid container of constant volume; the pressure of the gas is also kept constant. If the original rms speed of the gas molecules is 900 m/s, what would be the final rms speed if the number of particles in the gas is doubled?
Chapter 17 Solutions
Physics for Scientists and Engineers
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- If one kind of molecule has double the radius of another and eight times the mass, how do their mean free paths under the same conditions compare? How do their mean free times compare?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_forwardWhat is the average velocity of the air molecules in the room where you are right now?arrow_forward
- What is the total translational kinetic energy of the air molecules in a room of volume 23 m3 if the pressure is 9.5104 Pa (the room is at fairly high elevation) and die temperature is 21 ? Is any item of data unnecessary for the solution?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_forwardFrom 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.arrow_forward
- Under what circumstances would you expect a gas to behave significantly differently than predicted by the ideal gas law?arrow_forwardUsing the approximation v1v1+v f(v)dvf(v1)v for small v , estimate the fraction of nitrogen molecules at a temperature of 3.00102 K that have speeds between 290 m/s and 291 m/s.arrow_forwardA metallic container of fixed volume of 2.5103 m3 immersed in a large tank of temperature 27 contains two compartments separated by a freely movable wall. Initially, the wall is kept in place by a stopper so that there are 0.02 mol of the nitrogen gas on one side and 0.03 mol of the oxygen gas on the other side, each occupying half the volume. When the stopper is removed, the wall moves and comes to a final position. The movement of the wall is controlled so that the wall moves in infinitesimal quasi-static steps. (a) Find the final volumes of the two sides assuming the ideal gas behavior for the two gases. (b) How much work does each gas do on the other? (c) What is the change in the internal energy of each gas? (d) Find the amount of heat that enters or leaves each gas.arrow_forward
- Calculate the total number of degrees of freedom possessed by the molecules in 1cm3 of H2 gas at NTP.arrow_forwardObtain the most probable distribution of N molecules of an ideal gas contained in two equal and connected volumes at the same temperature by minimizing the Helmholtz free energy for the two systems.arrow_forwardIn an ultrahigh vacuum system (with typical pressures lower than 10-7 pascal), the pressure is measured to be 1.00 x 10-10 torr (where 1 torr = 133 Pa). Assuming the temperature is 310 K, find the number of molecules in a volume of 1.00 m3.arrow_forward
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