College Physics
10th Edition
ISBN: 9781285737027
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Chapter 10.5, Problem 10.6QQ
To determine
The rms speed.
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At what temperature would the rms speed of helium atoms equal (a) the escape speed from Earth, 1.12 x 104 m/s and (b) the escape speed from the Moon, 2.37 x 103 m/s? Note: The mass of a helium atom is 6.64 x 10-27 kg.
An argon-40 atom has a mass of 6.64 ✕ 10−26 kg.
(a)
What temperature (in K) would a gas composed entirely of argon-40 atoms have to be at in order for the rms speed of the atoms to equal the escape speed from Earth, 1.12 ✕ 104 m/s?
K
(b)
What temperature (in K) would a gas composed entirely of argon-40 atoms have to be at in order for the rms speed of the atoms to equal the escape speed from the Moon, 2.37 ✕ 103 m/s?
K
An argon-40 atom has a mass of 6.64 ✕ 10−26 kg.
(a) What temperature (in K) would a gas composed entirely of argon-40 atoms have to be at in order for the rms speed of the atoms to equal the escape speed from Earth, 1.12 ✕ 104 m/s?
(b) What temperature (in K) would a gas composed entirely of argon-40 atoms have to be at in order for the rms speed of the atoms to equal the escape speed from the Moon, 2.37 ✕ 103 m/s?
Chapter 10 Solutions
College Physics
Ch. 10.1 - Prob. 10.1QQCh. 10.3 - If you quickly plunge a room-temperature mercury...Ch. 10.3 - If you are asked to make a very sensitive glass...Ch. 10.3 - Two spheres are made of the same metal and have...Ch. 10.3 - Prob. 10.5QQCh. 10.5 - Prob. 10.6QQCh. 10 - Prob. 1WUECh. 10 - Prob. 2WUECh. 10 - Prob. 3WUECh. 10 - An electrician is wiring new electrical outlets in...
Ch. 10 - Prob. 5WUECh. 10 - A cylinder of volume 50.0 cm3 made of Pyrex glass...Ch. 10 - One way to cool a gas is to let it expand. When a...Ch. 10 - A container holds 0.500 m3 of oxygen at an...Ch. 10 - Suppose 26.0 g of neon gas are stored in a tank at...Ch. 10 - Prob. 10WUECh. 10 - (a) Why does an ordinary glass dish usually break...Ch. 10 - Some thermometers are made of a mercury column in...Ch. 10 - Prob. 4CQCh. 10 - Objects deep beneath the surface of the ocean are...Ch. 10 - Why do vapor bubbles in a pot of boiling water get...Ch. 10 - Markings to indicate length are placed on a steel...Ch. 10 - Metal lids on glass jars can often be loosened by...Ch. 10 - Suppose the volume of an ideal gas is doubled...Ch. 10 - An automobile radiator is filled to the brim with...Ch. 10 - When the metal ring and metal sphere in Figure...Ch. 10 - Prob. 1PCh. 10 - The pressure in a constant-volume gas thermometer...Ch. 10 - Prob. 3PCh. 10 - Death Valley holds the record for the highest...Ch. 10 - Show that the temperature 40 is unique in that it...Ch. 10 - Prob. 6PCh. 10 - Show that if the temperature on the Celsius scale...Ch. 10 - The temperature difference between the inside and...Ch. 10 - Prob. 9PCh. 10 - Prob. 10PCh. 10 - Prob. 11PCh. 10 - A grandfather clock is controlled by a swinging...Ch. 10 - A pair of eyeglass frames are made of epoxy...Ch. 10 - A spherical steel ball bearing has a diameter of...Ch. 10 - A brass ring of diameter 10.00 cm at 20.0C is...Ch. 10 - Prob. 16PCh. 10 - Lead has a density of 11.3 103 kg/m3 at 0C. (a)...Ch. 10 - The Golden Gate Bridge in San Francisco has a main...Ch. 10 - An underground gasoline tank can hold 1.00 103...Ch. 10 - Show that the coefficient of volume expansion, ,...Ch. 10 - A hollow aluminum cylinder 20.0 cm deep has an...Ch. 10 - A construction worker uses a steel tape to measure...Ch. 10 - The hand in Figure P10.23 is stainless steel...Ch. 10 - The Trans-Alaskan pipeline is 1 300 km long,...Ch. 10 - The average coefficient of volume expansion for...Ch. 10 - The density or gasoline is 7.30 102 kg/m3 at 0C....Ch. 10 - Figure P10.27 shows a circular steel casting with...Ch. 10 - The concrete sections of a certain superhighway...Ch. 10 - Prob. 29PCh. 10 - A 20.0-L tank of carbon dioxide gas (CO2) is at a...Ch. 10 - (a) An ideal gas occupies a volume of 1.0 cm3 at...Ch. 10 - An automobile tire is inflated with air originally...Ch. 10 - Prob. 33PCh. 10 - Gas is contained in an 8.00-L vessel at a...Ch. 10 - Prob. 35PCh. 10 - The density of helium gas at 0C is 0 = 0.179...Ch. 10 - An air bubble has a volume of 1.50 cm3 when it is...Ch. 10 - The ideal gas law can be recast in terms of the...Ch. 10 - What is the average kinetic energy of a molecule...Ch. 10 - A sealed cubical container 20.0 cm on a side...Ch. 10 - Prob. 41PCh. 10 - Prob. 42PCh. 10 - Prob. 43PCh. 10 - A 7.00-L vessel contains 3.50 moles of ideal gas...Ch. 10 - Prob. 45PCh. 10 - Prob. 46PCh. 10 - Inside the wall of a house, an L-shaped section of...Ch. 10 - The active element of a certain laser is made of a...Ch. 10 - A popular brand of cola contains 6.50 g of carbon...Ch. 10 - Prob. 50APCh. 10 - Prob. 51APCh. 10 - A 1.5-m-long glass tube that is closed at one end...Ch. 10 - Prob. 53APCh. 10 - A vertical cylinder of cross-sectional area A is...Ch. 10 - Prob. 55APCh. 10 - Prob. 56APCh. 10 - A liquid with a coefficient of volume expansion of...Ch. 10 - Before beginning a long trip on a hot day, a...Ch. 10 - Two concrete spans of a 250-m-long bridge are...Ch. 10 - An expandable cylinder has its top connected to a...Ch. 10 - A bimetallic strip of length L is made of two...Ch. 10 - A 250-m-long bridge is improperly designed so that...Ch. 10 - Prob. 63APCh. 10 - Two small containers, each with a volume of 1.00 ...
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- One 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_forwardDecades ago, it was thought that huge herbivorous dinosaurs such as Apatosaurus and Brachiosaurus habitually walked on the bottom of lakes, extending their long necks up to the surface to breathe. Brarhiosaurus had its nostrils on the top of its head. In 1977, Knut Schmidt-Nielsen pointed out that breathing would be too much work for such a creature. For a simple model, consider a sample consisting of 10.0 L of air at absolute pressure 2.00 atm, with density 2.40 kg/m3, located at the surface of a freshwater lake. Find the work required to transport it to a depth of 10.3 m, with its temperature, volume, and pressure remaining constant. This energy investment is greater than the energy that can be obtained by metabolism of food with the oxygen in that quantity of air.arrow_forwardA sample of a monatomic ideal gas occupies 5.00 L at atmospheric pressure and 300 K (point A in Fig. P21.65). It is warmed at constant volume to 3.00 atm (point B). Then it is allowed to expand isothermally to 1.00 atm (point C) and at last compressed isobarically to its original state, (a) Find the number of moles in the sample. Find (b) the temperature at point B, (c) the temperature at point C, and (d) the volume at point C. (e) Now consider the processes A B, B C, and C A. Describe how to carry out each process experimentally, (f) Find Q, W, and Eint for each of the processes, (g) For the whole cycle A B C A, find Q, W, and Eint.arrow_forward
- The air we breathe is largely composed of nitrogen (N2) and oxygen (O2) molecules. The mass of an N2 molecule is less than the mass of an O2 molecule. (a) For air at 300 K, is the average kinetic energy of an N2 molecule greater than, less than, or equal to the average kinetic energy of an O2 molecule? (b) Is the rms speed in air of an N2 molecule greater than, less than, or equal to the rms speed in air of an O2 molecule?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_forwardFifteen identical particles have various speeds: one has a speed of 2.00 m/s, two have speeds of 3.00 m/s, three have speeds of 5.00 m/s, four have speeds of 7.00 m/s, three have speeds of 9.00 m/s, and two have speeds of 12.0 m/s. Find (a) the average speed, (b) the rms speed, and (c) the most probable speed of these particles.arrow_forward
- 2 4 3. What is the average (rms) speed of the molecules of a helium gas at a temperature of 23°C? m/s Y on N 2 W S #3 X command E с D $ 4 C R LL F G Search or type URL de 5 % V T G MacBook Pro 6 B Y H & 7 N U J ☆ * 00 8 M 1 + ( 6. K 9 O Δ· I : ; optionarrow_forwardIf the pressure of an ideal monatomic gas is increased while the number of moles is kept constant, what happens to the average translational kinetic energy of one atom of the gas? Is it possible to change both the volume and the pressure of an ideal gas and keep the average translational kinetic energy of the atoms constant? Explain.arrow_forwardFour tanks A, B, C, and D are filled with monatomic ideal gases. For each tank, the mass of an individual atom and the rms speed of the atoms are expressed in terms of m and Vrms respectively (see the table). Suppose that m = 2.23 x 10-26 kg, and Vrms = 1050 m/s. Find the temperature of the gas in each tank. (a) TA= (b) TB= (c) Tc = i i i i (d) TD= Mass Rms speed A m Urms B m 20rms C 2m Urms D 2m 20rmsarrow_forward
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