Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 20, Problem 26PQ
(a)
To determine
Sketch the speed distribution for which the most probable speed is equal to the average speed.
(b)
To determine
Sketch the speed distribution for which the most probable speed is greater than the average speed.
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Chapter 20 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 20.2 - In Example 20.1, we found that the rms value of a...Ch. 20.3 - If the temperature of a gas is doubled, what...Ch. 20.3 - Prob. 20.3CECh. 20.5 - Prob. 20.4CECh. 20.7 - Prob. 20.5CECh. 20.8 - Prob. 20.6CECh. 20 - Prob. 1PQCh. 20 - Prob. 2PQCh. 20 - Prob. 3PQCh. 20 - Prob. 4PQ
Ch. 20 - Prob. 5PQCh. 20 - Prob. 6PQCh. 20 - Prob. 7PQCh. 20 - Prob. 8PQCh. 20 - Particles in an ideal gas of molecular oxygen (O2)...Ch. 20 - Prob. 10PQCh. 20 - Prob. 11PQCh. 20 - Prob. 12PQCh. 20 - Prob. 13PQCh. 20 - Prob. 14PQCh. 20 - The mass of a single hydrogen molecule is...Ch. 20 - Prob. 16PQCh. 20 - The noble gases neon (atomic mass 20.1797 u) and...Ch. 20 - Prob. 18PQCh. 20 - Prob. 19PQCh. 20 - Prob. 20PQCh. 20 - Prob. 22PQCh. 20 - Prob. 23PQCh. 20 - Prob. 24PQCh. 20 - Prob. 25PQCh. 20 - Prob. 26PQCh. 20 - Prob. 27PQCh. 20 - Prob. 28PQCh. 20 - Consider the Maxwell-Boltzmann distribution...Ch. 20 - Prob. 30PQCh. 20 - Prob. 31PQCh. 20 - Prob. 32PQCh. 20 - Prob. 33PQCh. 20 - Prob. 34PQCh. 20 - Prob. 35PQCh. 20 - Prob. 36PQCh. 20 - Prob. 37PQCh. 20 - Prob. 38PQCh. 20 - Prob. 39PQCh. 20 - Prob. 40PQCh. 20 - Prob. 41PQCh. 20 - Prob. 42PQCh. 20 - Prob. 43PQCh. 20 - Prob. 44PQCh. 20 - Figure P20.45 shows a phase diagram of carbon...Ch. 20 - Prob. 46PQCh. 20 - Prob. 47PQCh. 20 - Consider water at 0C and initially at some...Ch. 20 - Prob. 49PQCh. 20 - Prob. 50PQCh. 20 - Prob. 51PQCh. 20 - Prob. 52PQCh. 20 - Prob. 53PQCh. 20 - Prob. 54PQCh. 20 - Prob. 55PQCh. 20 - Prob. 56PQCh. 20 - Consider again the box and particles with the...Ch. 20 - Prob. 58PQCh. 20 - The average kinetic energy of an argon atom in a...Ch. 20 - For the exam scores given in Table P20.60, find...Ch. 20 - Prob. 61PQCh. 20 - Prob. 62PQCh. 20 - Prob. 63PQCh. 20 - Prob. 64PQCh. 20 - Prob. 65PQCh. 20 - Prob. 66PQCh. 20 - Determine the rms speed of an atom in a helium...Ch. 20 - Consider a gas filling two connected chambers that...Ch. 20 - Prob. 69PQCh. 20 - Prob. 70PQCh. 20 - A 0.500-m3 container holding 3.00 mol of ozone...Ch. 20 - Prob. 72PQCh. 20 - Prob. 73PQ
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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_forwardWhat is the average velocity of the air molecules in the room where you are right now?arrow_forwardSuppose you have helium atoms in a sealed container and 20% of the atoms have a speed of 2.1 × 102 m/s and 80% have speed of 4.2 × 102 m/s. The atoms then collide with one another until the Maxwell-Boltzmann distribution is established. What is the temperature of the gas at equilibrium? Assume there is no heat exchange between the gas and the environment.arrow_forward
- What is the temperature (in Kelvin) of a sample of neon with an rms speed of 500.0 m/s?arrow_forwardItem at position 1 At the same pressure, the ideal gas law is density x temperature = constant. An old house has only one thermostat upstairs set at 20 deg C. The air density upstairs is 1.2 kg/m3, while downstairs is 3% denser. The air temperature downstairs is _____ °C.arrow_forwardFigure CQ10.9 shows Maxwell speed distributions for three different samples of oxygen (O2) gas. (a) Is the temperature of sample B greater than, less than, or equal to the temperature of sample A? (b) Is the temperature of sample C greater than, less than, or equal to the temperature of sample A?arrow_forward
- Two containers are at the same temperature. The first contains gas with pressure p1, molecular mass m1, and rms speed vrms1. The second contains gas with pressure 2.0p1, molecular mass m2, and average speed vavg2 = 2.0vrms1. Find the mass ratio m1/m2.arrow_forwardTwo moles of a helium gas are at a temperature of 260 K. Calculate the average kinetic energy per atom, the root-mean-square (rms) speed of atoms in the gas, and the internal energy of the gas. HINT (a) the average kinetic energy per atom (in J) J (b) the root-mean-square (rms) speed (in m/s) of atoms in the gas m/s (c) the internal energy of the gas (in J) Jarrow_forwardMars has an atmosphere composed almost entirely of carbon dioxide, with an average temperature of -63 ∘C∘�. You may want to review (Pages 360 - 366) . Part A What is the rms speed of a molecule in Mars's atmosphere? Assume R� = 8.315 J/mol⋅KJ/mol⋅K.arrow_forward
- Water expands when it freezes. How much work does 100. g of water do when it freezes at 0oC and bursts a water pipe that exerts an opposing pressure of 1070 atm? The densities of water and ice at 0 oC are 1.00 g/cm3 and 0.92 g/cm3, respectively. Observe proper number of significant figures.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_forwardWhich of the following describes a real gas better? A) gas particles repel each other B) all collisions are elastic C) gas particles are very tiny, but they are not infinitely small (D) gas particles behave according to pV=nRT.arrow_forward
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