Pearson eText -- Physics for Scientists and Engineers with Modern Physics -- Instant Access (Pearson+)
5th Edition
ISBN: 9780137488179
Author: Douglas Giancoli
Publisher: PEARSON+
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77 SSM Figure 19-28 shows a hy-
pothetical speed distribution for
particles of a certain gas: P(v) = Cv2
for 0
Vg. Find (a) an expression for C in
terms of vo, (b) the average speed of
the particles, and (c) their rms speed.
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Vo
Speed
Figure 19-28 Problem 77.
(4)d
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)
(a) Compute the rms speed of a nitrogen molecule at 20.0C.The molar mass of nitrogen molecules (N2) is given in Table 19-1.At what temperatures will the rms speed be (b) half that value and(c) twice that value?
Chapter 18 Solutions
Pearson eText -- Physics for Scientists and Engineers with Modern Physics -- Instant Access (Pearson+)
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_forwardFrom the MaxwellBoltzmann speed distribution, show that the most probable speed of a gas molecule is given by Equation 16.23. Note: The most probable speed corresponds to the point at which the slope of the speed distribution curve dNv/dv is zero.arrow_forwardi) In a cylinder 4 moles of Helium gas (M= 4.02 x 103 kg/mole) is at 30 °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
- 49. (11) We saw in Example 18-8 that the mean free path &M of air molecules at STP is about 9 x 108 m. Estimate the collision frequency f, the number of collisions per unit time.arrow_forwardWhat is the average translational kinetic energy of an ideal-gas molecule at 27C? (b) What is the total random translational kinetic energy of the molecules in 1 mole of this gas? (c) What is the rms speed of oxygen molecules at this temperature?arrow_forwardASAParrow_forward
- 3) 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_forward57. ssm Initially, the translational rms speed of a molecule of an ideal gas is 463 m/s. The pressure and volume of this gas are kept constant, while the number of molecules is doubled. What is the final translational rms speed of the molecules?arrow_forwardEstimate the time needed for a glycine molecule (see Table 13−413−4 in the textbook) to diffuse a distance of 27 μmμm in water at 20 ∘C∘C if its concentration varies over that distance from 1.16 mol/m3mol/m3 to 0.40 mol/m3mol/m3 . Compare this "speed" to its rms (thermal) speed. The molecular mass of glycine is about 75 u. vdiffusevrmsvdiffusevrms =arrow_forward
- 17 In Fig. 20-25, where V23 = 3.00V1, n moles of a diatomic ideal gas are taken through the cycle with the molecules rotating but not oscil- lating. What are (a) pz/p1- (b) P3/P1, and (c) T3/T? For path 1 2, what are (d) W/NRT,, (e) QinRT, (f) AEm/nRT, and (g) AS/nR? For path 2→ 3, what are (h) W/nRT, (i) QinRT,, (j) AEin/NRT1, (k) AS/nR? For path 3 → 1, what are (1) W/NRT,, (m) QinRT,, (n) AEin/nRT1, and (o) AS/nR? Isothermal Adiabatic 2. Vas Vị Volume Figure 20-25 Problem 17. Pressurearrow_forwardA box of 10.0 cm x 10.0 cm x 10.0 cm contains 1.2 x 105 Pa of N2 gas molecules at 25°C. The mass of one N2 molecule is 4.68 x 10-26 kg and its molar mass is 28.0-g Assume all the molecules collide with the container walls with its rms speed in a head-on fashion and all the collisions are perfectly elastic, estimate the amount of molecules striking one side of the container wall in 10 seconds? (R = 8.31 J/mole/K -0.08205 Latm/mole/K, kg-1.38 X 10 23 J/K, 1 atm = 1.01X 105 Pa.) 4.1 x 1028 2.9 x 1026 3.2 x 1020 7.5 x 1022 10 x 1024 A Question 21 (4 points) Retake question I used equations in the list to solve the above problem: AT P = k₁A₁AT¹ + k2A22 + k3A3 P = KAAT AT3 L3 P = E/t P = AAT +AT+ A 1. Yes. 2. No. P=A- AT R₁+Ra+R3arrow_forwardDetermine the average value of the translational kinetic energy of the molecules of an ideal gas at temperatures (a) 0.00C and (b) 100C.What is the translational kinetic energy per mole of an ideal gas at (c) 0.00C and (d) 100C?arrow_forward
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