Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Question
Chapter 17, Problem 61P
To determine
The rms speed and kinetic energy of hydrogen gas molecules.
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In the hot gases of an automotive engine's cylinders, temperatures may exceed 3100 k. What would be the "root mean square" or "rms" velocity of a hydrogen atom, if one happened to be in that gas after some chemical reaction? The mass of a hydrogen atom is about 1.66x10-27 kg. Give your answer in m/s, but enter only the number.
At what temperature do atoms of helium gas have the same rms speed as molecules of hydrogen gas at 20.0C?
If the temperature of an ideal gas is raised from 15C to 250C, how many times faster is the new average (rms) speed of the gas molecules?
Chapter 17 Solutions
Physics for Scientists and Engineers
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- Eight bumper cars, each with a mass of 322 kg. are running in a room 21.0 m long and 130 m wide. They have no driver, so they just bounce around on their own. The rms speed of the cars is 2.50 m/s. Repeating the arguments of Pressure, Temperature, and RMS Speed, find the average force per unit length (analogous to Pressure) that the cars exert the walls.arrow_forwardCheck Your Understanding If you consider a very small object, such as a grain of pollen, in a gas, then the number of molecules striking its surface would also be relatively small. Would you expect the grain of pollen to experience any fluctuations in pressure due to statistical fluctuations in the number of gas molecules striking it in a given amount of time?arrow_forwardWhat is the average velocity of the air molecules in the room where you are right now?arrow_forward
- 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_forwardConsider again the box and particles with the speed distribution described in Problem 56. a. What is the average pressure exerted by the particles on the walls of the box? b. What is the average kinetic energy per particle in this box?arrow_forwardAverage atomic and molecular speeds (vrms) are large, even at low temperatures. What is vrms for helium atoms at 5.00 K, just one degree above helium's liquefaction temperature?arrow_forward
- Suppose that the average velocity (vrms) of carbon dioxide molecules (molecular mass is equal to 44.0g/mol ) in a ?ame is found to be 1.05105m/s. What temperature does this represent?arrow_forwardSome incandescent light bulbs are filled with argon, because it is an inert gas.An argon atom has a mass of 6.63 ×10−26 kg. What is the rms speed, in meters per second, for argon atoms near the filament, assuming their temperature is 2350 K?arrow_forwardThe rms speed of a certain sample of ammonia molecules, with a molecular weight of 17 g/mol, is 328 m/s. What is the rms speed of carbon monoxide molecules, with a molecular weight of 28 g/mol, at the same temperature?arrow_forward
- Calculate the rms speed of helium atoms near the surface of the Sun at a temperature of about 5300 K . Express your answer to two significant figures and include the appropriate units.arrow_forwardOxygen, modeled as an ideal gas, is in a container and has a temperature of 77.0°C. What is the rms-average magnitude of the momentum of the gas molecules in the container?arrow_forwardEight bumper cars, each with a mass of 322 kg, are running in a room 21.0 m long and 13.0 m wide. They have no drivers, so they just bounce around on their own. The rms speed of the cars is 2.50 m/s. Repeating the argumentsof Pressure, Temperature, and RMS Speed, find the average force per unit length (analogous to pressure) that the cars exert on the walls.arrow_forward
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