Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 20, Problem 10P
To determine
A phase diagram for carbon dioxide.
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Chapter 20 Solutions
Physics for Scientists and Engineers
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- 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_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_forwardWhat 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_forward
- An ideal gas has a pressure of 0.50 atm and a volume of 10 L. It is compressed adiabatically and quasi-statically until its pressure is 3.0 atm and its volume is 2.8 L. Is the monatomic, diatomic, or polyatomic?arrow_forwardHow much volume does a half mole of ideal gas occupies at standard ambient temperature and pressure?arrow_forwardThe only form of energy possessed by molecules of a monatomic ideal gas is translational kinetic energy. From kinetic, the average kinetic energy per molecule is KEmolecule = 3 2 kBT = 3 2 R NA T Use these results to show that the internal energy of a monatomic ideal gas at pressure P and occupying volume V may be written as U = 3 2 PV.arrow_forward
- The only form of energy possessed by molecules of a monatomic ideal gas is translational kinetic energy. Using the results from the discussion of kinetic theory in Section 10.5, show that the internal energy of a monatomic ideal gas at pressure P and occupying volume V may be written as U = 3/2PVarrow_forwardDon't Copy. The specific heat at constant volume at -200°C of one mole of an ideal diatomic gas isA) 1/2 R. B) R. C) 3/2 R . D)2R. E) I don’t knowarrow_forwardCalculate the Helmholtz free energy (∆A) of an ideal gas when 2.0 mol expands isothermally from 1.5 to 3.5 cm3 at 120°Carrow_forward
- Calculate ΔG when supercooled water at –3oC freezes at constant P and T. The vapor pressure of ice at –3oC is 475 Pa, and the vapor pressure of supercooled water at –3oC is 489 Pa. Answer: - 65.2arrow_forwardCalculate the root-mean-square (rms) speed of methane (CH4) gas molecules at a temperature of 325 K.arrow_forwardThe best laboratory vacuum has a pressure of about 1.00 * 10-18 atm, or 1.01 * 10-13 Pa. How many gas molecules are there per cubic centimeter in such a vacuum at 293 K?arrow_forward
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