Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 17, Problem 63P
To determine
The mean free path for a molecule in an ideal gas.
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By what factor does the rms speed of a molecule change if the temperature is increased from 24 °C to 1000 °C?
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The mean free path λ and the mean collision time T of molecules of a diatomic gas with molecular mass 6.00 x10^-25 kg and radius r=1.0x10^-10m are measured.From these microscopic data we can obtain macroscopic properties such as temperature T and pressure P? If yes, consider λ=4.32x10^-8m and T=3.00x10^-10s and calculate T and P.a)It's not possible.b)Yes,T=150K and P~2.04atm.c)Yes,T=150K and P~4.08atm.d)Yes,T=300K and P~4.08atm.e)Yes,T=300K and P~5.32atmf)Yes,T=400K and P~4.08atmg)Yes,T=400K and P~5.32atm.
The speed of a molecule in a uniform gas at equilibrium is a random variable V whose density function is given
by
S(0) = av²e-b*;
D > 0,
where b = m/(2kT) and k, T and m denote Boltzmann's constant, the absolute temperature, and the mass of the
molecule, respectively.
(a) Derive the distribution of W = mV² /2, the kinetic energy of the molecule.
(b) Find E (W).
Chapter 17 Solutions
Physics for Scientists and Engineers
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- A gas is at 200 K. If we wish to double the rms speed of the molecules of the gas, to what value must we raise its temperature? (a) 283 K (b) 400 K (c) 566 K (d) 800 K (e) 1 130 Karrow_forwardFind the ratio f(vp)/f(vrms) for hydrogen gas ( M=2.02 g/mol) at a temperature of 77.0 K.arrow_forwardYou measure the average free path λ and the average collision time τ of the molecules of a diatomic gas of molecular mass 6.00 × 10-²⁵ kg and radius r = 1.0 x 10-¹⁰ m. From these microscopic data can we obtain macroscopic properties such as temperature T and pressure P? If so, consider λ = 4.32 x 10-⁸ m and τ = 3.00 x 10-¹⁰ s and calculate T and P. indicate the correct answer: 1- Not possible2- Yes, T =150 K and P ~ 2.04 atm.3- Yes, T = 150 K and P ~ 4.08 atm.4- Yes, T = 300 K and P ~ 4.08 atm.5- Yes, T = 300 K and P ~ 5.32 atm6- Yes, T = 400 K and P ~ 4.08 atm.7- Yes, T = 400 K and P ~ 5.32 atm. obs.: If necessary, consider: R = 8.314 J/mol∙K1 cal = 4.19 Jkb =1,38 x 10⁻²³ m² kg s⁻² K⁻¹arrow_forward
- The air is a gas mixture of oxygen, carbon dioxide, and Nitrogen. If the air can be treated as ideal gas at temperature 100 °C, what is the average kinetic energy for each of the molecule in air?(Consider Oxygen, Nitrogen, and carbon dioxide as diatomic molecule structure which consist of translational and rotational degree of freedom only. No vibration motion is considered) Boltzmann constant is kg 1. 38 x 10-231/Karrow_forwardShow that the RMS velocity of gas molecule is directly proportional to square root of its absolute temperature.arrow_forwardThe pressure unit 1 torr is comparable to 0.001 bar. In a sample of N₂ at this pressure and a temperature of 300 K, what is the mean free path between collisions in mm (millimeters)? Assume that the cross-section for N₂ molecules is o = 4.50 × 10-19 m².arrow_forward
- At what temperature will the rms speed of a molecule is quarter of that of it has at a temperature of 1270c?arrow_forwardA sample of 6 moles of an ideal diatomic gas experiences a temperature increase of 150 K at constant volume. (a) Find the increase in internal energy if only translational and rotational motions are possible. 15706.5 X J (b) Find the increase in internal energy if translational, rotational, and vibrational motions are possible. 22447.8 X J (c) What fraction of the energy calculated in (b) is translational kinetic energy? 0.6 xarrow_forwardUnder the Equipartition Principle, in the high temperature limit, molecular heat capacity should be 1 -NR, where N is the number of atoms in 2 the molecule and R is the gas constant. O True O Falsearrow_forward
- The gas of oxygen at temperature 100 °C can be treated as ideal gas. (a)What is the internal energy of the gas? (b) what is the average translational kinetic energy for each of the oxygen molecule? (Consider Oxygen as diatomic molecule structure which consists of translational and rotational degree of freedom only. No vibration motion is considered) Boltzmann constant is kg = 1.38 × 10-23J/Karrow_forwardInterstellar space is quite different from the gaseous environments we commonly encounter on Earth. For instance, a typical density of the medium is about 1 atom cm−3 and that atom is typically H; the effective temperature due to stellar background radiation is about 10 kK. Estimate the diffusion coefficient and thermal conductivity of H under these conditions. Compare your answers with the values for gases under typical terrestrial conditions. Comment: Energy is in fact transferred much more effectively by radiation.arrow_forwardAssuming the radius of diatomic molecules is approximately 1.0 x 10-10 m, for what pressure will the mean free path in room-temperature (20°C) nitrogen be 4.6 m?arrow_forward
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