Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
12th Edition
ISBN: 9781259587399
Author: Eugene Hecht
Publisher: McGraw-Hill Education
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Chapter 17, Problem 22SP
To determine
To show: The total translational kinetic energy of a gas containing
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Hi, could I get some help with this micro-macro connection physics problem involving root mean square speed?
The set up is:
For an atom in an ideal gas with rms speed in one direction, vx = 100 m/s, and mass m = 6.66e-27 kg, what is the temperature T in kelvin (K) to four digits of precision if Boltzman constant kB = 1.38e-23 J/K?
Thank you.
What properties of a nonideal gas do the van der Waals constants a and b represent?
Although an ordinary H2 molecule consists of two identical atoms, this is not the case for the molecule HD, with one atom of deuterium (Le., heavy hydrogen, 2H). Because of its small moment of inertia, the HD molecule has a relatively large value of E: 0.0057 eV. At approximately what temperature would you expect the rotational heat capacity of a gas of HD molecules to "freeze out," that is, to fall significantly below the constant value predicted by the equipartition theorem?
Chapter 17 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
Ch. 17 - Prob. 13SPCh. 17 - 17.14 [II] A typical polymer molecule in...Ch. 17 - 17.15 [II] A certain strain of tobacco mosaic...Ch. 17 - 17.16 [I] If the Celsius temperature of a gas...Ch. 17 - 17.17 [I] What happens to the average kinetic...Ch. 17 - 17.18 [I] The absolute temperature of a sample of...Ch. 17 - Prob. 19SPCh. 17 - Prob. 21SPCh. 17 - Prob. 22SPCh. 17 - Prob. 23SP
Ch. 17 - Prob. 24SPCh. 17 - Prob. 25SPCh. 17 - Prob. 26SPCh. 17 - Prob. 27SPCh. 17 - Prob. 28SPCh. 17 - 17.29 [II] In a certain region of outer space...Ch. 17 - 17.30 [II] A cube of aluminum has a volume of 1.0 ...Ch. 17 - 17.31 [II] The rms speed of nitrogen molecules in...Ch. 17 - 17.32 [II] What is the mean free path of a gas...
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- How does the Boltzmann distribution and statistics explain the behavior of an ideal gas in terms of the distribution of molecular energies and the probability of various energy states?arrow_forwardWhen are the rotational degrees of freedom of a diatomic molecule expected to contribute R to the molar constant volume heat capacity? When will a vibrational degree of freedom contribute R to the molar heat capacity?arrow_forwardLet's consider the three atoms composing the molecule now have different masses and coordinate, while the axis of rotation is still z axis that is perpendicular to the xy plane. The first atom has a mass of 142.54 kg, with x coordinate at 3 m and y coordinate at 6 m. The second atom has a mass of 82.55 kg, with x coordinate at 1 m and y coordinate at 6 m. The third atom has a mass of 8 kg, with x coordinate at 5 m and y coordinate at 9 m. What is the moment of inertia in unit of kg m2 with respect to the x axis?arrow_forward
- Consider air at P = 1.00 atm. The average molecular mass of air is approximately 29 u. Boltzmann constant is 1.380 × 10−23 J/K. What is the total translational kinetic energy of the gas molecules of air at atmospheric pressure that occupies a volume of 1.80 L (in J)?arrow_forwardEstimate the mean free path of a nitrogen molecule in a cylinder nitrogen at 2 atm and a temperature of 17 oC. Take the radius to be roughly equal to 1 x10-10 m. Boltzmann constant 1.38 x10-23 J/K.arrow_forwardConsider a dust grain in the shape of a very thin cylinder, floating in a gas at a temperature T. On average, will the angular momentum vector for this dust grain point nearly parallel or nearly perpenticular to its axis?arrow_forward
- Give the temperature T of 1 mole of ideal gas as a function of the pressure P, volume V, and the gas constant R and give the internal energy U of a rigid diatomic ideal gas as a function of its temperature T and the gas constant R.arrow_forwardOnly answer letters (d) and (e) a) Using the Maxwell-Boltzmann function, calculate the fraction of argon gas molecules with a speed of 305 m/s at 500 K. (ans: 0.0014) b) If the system in (a) has 0.46 moles of argon gas, how many molecules have the speed of 305 m/s? (ans: 6.44 x 10-4) c) Calculate the values of vmp, vavg, and vrms for xenon gas at 298 K. (ans: Vmp=194.2 m/s , Vavg=219.2 m/s , Vrms=237.8 m/s) d) From the values calculated in (c), label the Boltzmann distribution plot with the approximate locations of vmp, v avg, and vrms e) What will have a larger speed distribution, helium at 500 K or argon at 300 K? Helium at 300 K or argon at 500 K? Argon at 400 K or argon at 1000 K?arrow_forwardConsider two immiscible liquids such as water and oil. If a spherical oil molecule of radius r is taken out of the oil phase and placed in the water phase, the unfavorable energy of this transfer is proportional to the area of the solute (oil) molecule newly exposed to the solvent (water) multiplied by the interfacial energy, i, of the oil-water interface. The interfacial energy of the bulk cyclohexane-water interface is i = 50 mJ m-2, and the radius of a cyclohexane molecule is 0.28 nm. Using Boltzmann distribution, estimate the solubility of cyclohexane in water at 25 C in units of mol L-1.The concentration of water in water phase is 55.5 mol L-1.arrow_forward
- Hi, could I get some help with this micro-macro connection physics problem involving root mean square speed? The set up is: What is the rms speed (in m/s) of a helium-3 atom in an ideal gas at a room temperature of 300 kelvin (K) to 4 digits of precision if kB = 1.38e-23 J/K, and the mass of helium-3 is 3.016 u, where the atomic mass unit u = 1.66e-27 kg? Thank you.arrow_forwardHow to use Boltzmann factors to derive the exponential formula for the density of an isothermal atmosphere. (Hint: Let the system be a single air molecule, let 81 be a state with the molecule at sea level, and let 82 be a state with the molecule at height z)arrow_forwardIf NA is Avogadro's number, and kB is Boltzmann's constant, which of the following expressions correctly represents the ideal gas contant? a. b. c. d. e.arrow_forward
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