EBK PHYSICS FOR SCIENTISTS & ENGINEERS
5th Edition
ISBN: 9780134296074
Author: GIANCOLI
Publisher: VST
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(II) Show that the rms speed of molecules in a gas is given
by vrms = V3P/p, where P is the pressure in the gas and
pis the gas density.
ii)
In a cylinder 5 moles of Methane gas (M=16.04 x 10³ kg/mole) is at
35 °C
temperature.
Calculate for the gas: (R=8.31 J/kg-mole K and KB =1.38 x 10-23 J/K)
(a) the average kinetic energy of a molecule,
(b) the total random kinetic energy of all the molecules, and
(c) the rms speed of a molecule
(a) How many atoms of helium gas fill a spherical balloon of diameter 30.8 cm at 18.0°C and 1.00 atm?
atoms
(b) What is the average kinetic energy of the helium atoms?
]
(c) What is the rms speed of the helium atoms?
km/s
Chapter 18 Solutions
EBK PHYSICS FOR SCIENTISTS & ENGINEERS
Ch. 18.1 - Prob. 1AECh. 18.1 - Prob. 1BECh. 18.1 - Prob. 1CECh. 18.1 - Prob. 1DECh. 18.4 - Prob. 1EECh. 18 - Why doesnt the size of different molecules enter...Ch. 18 - When a gas is rapidly compressed (say, by pushing...Ch. 18 - In Section 181 we assumed the gas molecules made...Ch. 18 - Explain in words how Charless law follows from...Ch. 18 - Prob. 5Q
Ch. 18 - As you go higher in the Earths atmosphere, the...Ch. 18 - Prob. 7QCh. 18 - Explain why the peak of the curve for 310 K in...Ch. 18 - Is temperature a macroscopic or microscopic...Ch. 18 - Escape velocity for the Earth refers to the...Ch. 18 - Prob. 11QCh. 18 - If the pressure in a gas is doubled while its...Ch. 18 - What everyday observation would tell you that not...Ch. 18 - Alcohol evaporates more quickly than water at room...Ch. 18 - Explain why a hot humid day is far more...Ch. 18 - Is it possible to boil water at room temperature...Ch. 18 - What exactly does it mean when we say that oxygen...Ch. 18 - A length of thin wire is placed over a block of...Ch. 18 - Consider two days when the air temperature is the...Ch. 18 - (a) Why does food cook faster in a pressure...Ch. 18 - How do a gas and a vapor differ?Ch. 18 - (a) At suitable temperatures and pressures, can...Ch. 18 - Why does dry ice not last long at room...Ch. 18 - Under what conditions can liquid CO2 exist? Be...Ch. 18 - Why does exhaled air appear as a little white...Ch. 18 - Prob. 26QCh. 18 - Prob. 27QCh. 18 - Prob. 1MCQCh. 18 - Prob. 2MCQCh. 18 - Prob. 3MCQCh. 18 - Prob. 4MCQCh. 18 - Prob. 5MCQCh. 18 - Prob. 6MCQCh. 18 - Prob. 7MCQCh. 18 - Prob. 8MCQCh. 18 - Prob. 9MCQCh. 18 - Prob. 10MCQCh. 18 - Prob. 1PCh. 18 - Prob. 2PCh. 18 - Prob. 3PCh. 18 - Prob. 4PCh. 18 - Prob. 5PCh. 18 - Prob. 6PCh. 18 - (I) A 1.0-mol sample of hydrogen gas has a...Ch. 18 - Prob. 8PCh. 18 - Prob. 9PCh. 18 - Prob. 10PCh. 18 - Prob. 11PCh. 18 - Prob. 12PCh. 18 - Prob. 13PCh. 18 - Prob. 14PCh. 18 - Prob. 15PCh. 18 - Prob. 16PCh. 18 - Prob. 17PCh. 18 - Prob. 18PCh. 18 - Prob. 19PCh. 18 - (I) A group of 25 particles have the following...Ch. 18 - Prob. 21PCh. 18 - Prob. 22PCh. 18 - Prob. 24PCh. 18 - (I) (a) At atmospheric pressure, in what phases...Ch. 18 - Prob. 26PCh. 18 - Prob. 27PCh. 18 - Prob. 28PCh. 18 - Prob. 29PCh. 18 - Prob. 30PCh. 18 - Prob. 31PCh. 18 - Prob. 32PCh. 18 - (II) A pressure cooker is a sealed pot designed to...Ch. 18 - Prob. 34PCh. 18 - Prob. 35PCh. 18 - Prob. 36PCh. 18 - Prob. 37PCh. 18 - Prob. 38PCh. 18 - Prob. 39PCh. 18 - Prob. 40PCh. 18 - Prob. 41PCh. 18 - Prob. 42PCh. 18 - Prob. 43PCh. 18 - Prob. 44PCh. 18 - Prob. 45PCh. 18 - Prob. 46PCh. 18 - Prob. 47PCh. 18 - Prob. 49PCh. 18 - Prob. 53PCh. 18 - A sample of ideal gas must contain at least N =...Ch. 18 - In outer space the density of matter is about one...Ch. 18 - Calculate approximately the total translational...Ch. 18 - (a) Estimate the rms speed of an amino acid, whose...Ch. 18 - The escape speed from the Earth is 1.12 104 m/s,...Ch. 18 - Prob. 63GPCh. 18 - Prob. 66GPCh. 18 - Prob. 69GPCh. 18 - Prob. 71GPCh. 18 - Prob. 72GPCh. 18 - Prob. 73GPCh. 18 - Prob. 74GPCh. 18 - Prob. 75GPCh. 18 - Prob. 76GPCh. 18 - Prob. 77GP
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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_forwardCylinder A contains oxygen (O2) gas, and cylinder B contains nitrogen (N2) gas. If the molecules in the two cylinders have the same rms speeds, which of the following statements is false? (a) The two gases haw different temperatures. (b) The temperature of cylinder B is less than the temperature of cylinder A. (c) The temperature of cylinder B is greater than the temperature of cylinder A. (d) The average kinetic energy of the nitrogen molecules is less than the average kinetic energy of the oxygen molecules.arrow_forward(1) Calculate the rms (root-mean-square) speed of hydrogen (H2), helium (He), and oxygen (O2) at room temperature. These speeds are very high. Evaluate these speeds against the escape velocity from the Earth, ~11.2 [km/s].arrow_forward
- i) Evaluate rms speed, the average kinetic energy of a molecule and total random kinetic energy of all the molecules in 6 moles of air gas at a temperature of 700 K. (Molar mass of air is 28.97 x 10 ³ mole/kg, and kB = 1.38 x 10 23 J/K)arrow_forward(II) Is a gas mostly empty space? Check by assuming that the spatial extent of the gas molecules in air is about lo = 0.3 nm so one gas molecule occupies an approximate volume equal to l . Assume STP.arrow_forward(I) By what factor will the rms speed of gas moleculesincrease if the temperature is increased from 20°C to 160°C?arrow_forward
- (II) Show that for a mixture of two gases at the same tem- perature, the ratio of their rms speeds is equal to the inverse ratio of the square roots of their molecular masses, vi/v2 = VM,/M¡ .arrow_forward1. (a) Calculate a numerical value for the isothermal compressibility kT = -+ (), for air for summer in Albuquerque under the conditions of 0.83 atm and 311 K (100 °F), assuming ideal gas behavior. (b) The speed of sound is related to the isothermal compressibility via 1 Vsound p KT where the adiabatic exponenty = 7/5. Evaluate this expression to find the speed of sound in air (in meters per second, or in mph). It is helpful to note that the mass density p = (kg/mole) and molar density, i.e. the number of moles per cubic meter, which is the ratio n/V. You can use the ideal gas law PV = nRT to write the ratio n/V in terms of your known pressure P and known temperature T. The gas constant R = 8.314 J/(mole-Kelvin) or alternatively R = 0.08206 (liter-atm)/(mole- K). Standard temperature and pressure are 0 degrees C (273.15 K) and 1 atm (1.013×105 N/m²). A good estimate of M for air can be found by taking 20% of the molecular weight of oxygen and adding this to 80% of the molecular weight…arrow_forward3) In a cylinder 6 moles of natural gas (M-19.09 x 10* kg/mole) is at 40°C temperature. Calculate for the gas: (R-8.31 J/kg-mole K and KB -1.38 x 10-3 J/K) (a) the average kinetic energy of a molecule, (b) the total random kinetic energy of all the molecules, and (c) the rms speed of a moleculearrow_forward
- (a) An ideal gas occupies a volume of 1.4 cm3 at 20°C and atmospheric pressure. Determine the number of molecules of gas in the container. (b) If the pressure of the 1.4-cm3 volume is reduced to 3.0 ✕ 10−11 Pa (an extremely good vacuum) while the temperature remains constant, how many moles of gas remain in the container? molarrow_forward(a) An ideal gas occupies a volume of 2.6 cm3 at 20°C and atmospheric pressure. Determine the number of molecules of gas in the container. molecules (b) If the pressure of the 2.6-cm3 volume is reduced to 2.2 ✕ 10−11 Pa (an extremely good vacuum) while the temperature remains constant, how many moles of gas remain in the container? molarrow_forward(III) Calculate (a) the rms speed of an oxygen molecule at0°C and (b) determine how many times per second it wouldmove back and forth across a 5.0-m-long room on average,assuming it made no collisions with other molecules.arrow_forward
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