Fundamentals of Physics Extended
10th Edition
ISBN: 9781118230725
Author: David Halliday, Robert Resnick, Jearl Walker
Publisher: Wiley, John & Sons, Incorporated
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Textbook Question
Chapter 19, Problem 77P
SSM Figure 19-28 shows a hypothetical speed distribution for particle of a certain gas: P(v) = Cv2 for 0 < v ≤ v0 and P(v) = 0 for v > v0. Find (a) an expression for C in terms of v0, (b) the average speed of the particles, and (c) their rms speed.
Figure19-28 Problem 77.
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Figure 19-28 Problem 77.
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The following figure is a histogram showing the speeds of the molecules in a very small gas. What are (a) the most probable speed, (b) the average speed, and (c) the rms speed?
A)An ideal gas is confined to a container at a temperature of 330 K.What is the average kinetic energy of an atom of the gas? (Express your answer to two significant figures.)
B)2.00 mol of the helium is confined to a 2.00-L container at a pressure of 11.0 atm. The atomic mass of helium is 4.00 u, and the conversion between u and kg is 1 u = 1.661 ××10−27 kg.Calculate vrmsvrms. (Express your answer to three significant figures.)
C)A gold (coefficient of linear expansion α=14×10−6K−1α=14×10−6K−1 ) pin is exactly 4.00 cm long when its temperature is 180∘∘C. Find the decrease in long of the pin when it cools to 28.0∘∘C? (Express your answer to two significant figures.)
Chapter 19 Solutions
Fundamentals of Physics Extended
Ch. 19 - For four situations for an ideal gas, the table...Ch. 19 - In the p-V diagram of Fig. 19-17, the gas does 5 J...Ch. 19 - For a temperature increase of T1, a certain amount...Ch. 19 - The dot in Fig, 19-18a represents the initial...Ch. 19 - A certain amount of energy is to be transferred as...Ch. 19 - The dot in Fig. 19-18b represents the initial...Ch. 19 - a Rank the four paths of Fig. 19-16 according to...Ch. 19 - The dot in Fig. 19-18c represents the initial...Ch. 19 - Prob. 9QCh. 19 - Does the temperature of an ideal gas increase,...
Ch. 19 - Prob. 1PCh. 19 - Gold has a molar mass of 197 g/mol. a How many...Ch. 19 - SSM Oxygen gas having a volume of 1000 cm3 at...Ch. 19 - A quantity of ideal gas at: 10.0C and 100 kPa...Ch. 19 - The best laboratory vacuum has a pressure of about...Ch. 19 - Water bottle in a hot car. In the American...Ch. 19 - Suppose 1.80 mol of an ideal gas is taken from a...Ch. 19 - Compute a the number of moles and b the number of...Ch. 19 - An automobile tire has a volume of 1.64 102 m3...Ch. 19 - A container encloses 2 mol of an ideal gas that...Ch. 19 - SSM ILW WWW Air that initially occupies 0.140 m3...Ch. 19 - GO Submarine rescue. When the U.S. submarine...Ch. 19 - Prob. 13PCh. 19 - In the temperature range 310 K to 330 K, the...Ch. 19 - Suppose 0.825 mol of an ideal gas undergoes an...Ch. 19 - An air bubble of volume 20 cm3 is at the bottom of...Ch. 19 - GO Container A in Fig. 19-22 holds an ideal gas at...Ch. 19 - The temperature and pressure in the Suns...Ch. 19 - a Compute the rms speed of a nitrogen molecule at...Ch. 19 - Calculate the rms speed of helium atoms at 1000 K....Ch. 19 - SSM The lowest possible temperature in outer space...Ch. 19 - Find the rms speed of argon atoms at 313 K. See...Ch. 19 - A beam of hydrogen molecules H2 is directed toward...Ch. 19 - At 273 K and 1.00 102 atm, the density of a gas...Ch. 19 - Prob. 25PCh. 19 - Prob. 26PCh. 19 - Water standing in the open at 32.0C evaporates...Ch. 19 - At what frequency would the wavelength of sound in...Ch. 19 - SSM The atmospheric density at an altitude of 2500...Ch. 19 - Prob. 30PCh. 19 - In a certain particle accelerator, protons travel...Ch. 19 - Prob. 32PCh. 19 - Prob. 33PCh. 19 - Prob. 34PCh. 19 - Prob. 35PCh. 19 - The most probable speed of the molecules in a gas...Ch. 19 - Prob. 37PCh. 19 - Figure 19-24 gives the probability distribution...Ch. 19 - At what temperature does the rms speed of a...Ch. 19 - Two containers are at the same temperature. The...Ch. 19 - Prob. 41PCh. 19 - What is the internal energy of 1.0 mol of an ideal...Ch. 19 - Prob. 43PCh. 19 - GO One mole of ail ideal diatomic gas goes from a...Ch. 19 - ILW The mass of a gas molecule can be computed...Ch. 19 - Under constant pressure, the temperature of 2.00...Ch. 19 - The temperature of 2.00 mol of an ideal monatomic...Ch. 19 - GO When 20.9 J was added as heat to a particular...Ch. 19 - SSM A container holds a mixture of three...Ch. 19 - We give 70 J as heat to a diatomic gas, which then...Ch. 19 - Prob. 51PCh. 19 - GO Suppose 12.0 g of oxygen O2 gas is heated at...Ch. 19 - SSM WWW Suppose 4.00 mol of an ideal diatomic gas...Ch. 19 - We know that for an adiabatic process pV = a...Ch. 19 - A certain gas occupies a volume of 4.3 L at a...Ch. 19 - Suppose 1.00 L of a gas with = 1.30, initially at...Ch. 19 - The volume of an ideal gas is adiabatically...Ch. 19 - GO Opening champagne. In a bottle of champagne,...Ch. 19 - GO Figure 19-26 shows two paths that may be taken...Ch. 19 - GO Adiabatic wind. The normal airflow over the...Ch. 19 - GO A gas is to be expanded from initial state i to...Ch. 19 - GO An ideal diatomic gas, with rotation but no...Ch. 19 - Figure 19-27 shows a cycle undergone by 1.00 mol...Ch. 19 - Calculate the work done by an external agent...Ch. 19 - An ideal gas undergoes an adiabatic compression...Ch. 19 - Prob. 66PCh. 19 - An ideal monatomic gas initially has a temperature...Ch. 19 - Prob. 68PCh. 19 - SSM The envelope and basket of a hot-air balloon...Ch. 19 - An ideal gas, at initial temperature T1 and...Ch. 19 - Prob. 71PCh. 19 - At what temperature do atoms of helium gas have...Ch. 19 - Prob. 73PCh. 19 - Prob. 74PCh. 19 - The temperature of 3.00 mol of a gas with CV =...Ch. 19 - During a compression at a constant pressure of 250...Ch. 19 - SSM Figure 19-28 shows a hypothetical speed...Ch. 19 - Prob. 78PCh. 19 - SSM An ideal gas undergoes isothermal compression...Ch. 19 - Oxygen O2 gas at 273 K and 1.0 atm is confined to...Ch. 19 - An ideal pas is taken through a complete cycle in...Ch. 19 - Prob. 82PCh. 19 - SSM A sample of ideal gas expands from an initial...Ch. 19 - An ideal gas with 3.00 mol is initially in state 1...Ch. 19 - A steel lank contains 300 g of ammonia gas NH3 at...Ch. 19 - In an industrial process the volume of 25.0 mol of...Ch. 19 - Figure 19-29 shows a cycle consisting of five...Ch. 19 - An ideal gas initially at 300 K is compressed at a...Ch. 19 - A pipe of length L = 25.0 m that is open at one...Ch. 19 - In a motorcycle engine, a piston is forced down...Ch. 19 - For adiabatic processes in an ideal gas, show that...Ch. 19 - Air at 0.000C and 1.00 atm pressure has a density...Ch. 19 - Prob. 93PCh. 19 - Prob. 94PCh. 19 - Prob. 95PCh. 19 - For air near 0C, by how much does the speed of...Ch. 19 - Prob. 97P
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- Cylinder 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_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_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
- 38 Figure 19-24 gives the probability distribution for nitrogen gas. The scale of the horizontal axis is set by v, = 1200 m/s. What are the (a) gas temperature and (b) rms speed of the molecules? v (m/s) (A)darrow_forwardWhat is the value of the compressibility factor, Z. when the volume of 1 mol of a real gas is smaller than that of 1 mol of an ideal gas at constant pressure and temperature? 7 < 1 Z = 1 Z>1 Z cannot be determinedarrow_forward1.50 moles of a monatomic ideal gas goes isothermally from state 1 to state 2. P1 = 2.4×105 Pa, V1 = 64 m3, and P2 = 7.4×105 Pa. What is the volume in state 2, in m3?arrow_forward
- A sealed container contains a fixed volume of a monatomic ideal gas. If the gas temperature is increased by a factor of two, what is the ratio of the final to the initial (a) pressure, (b) average molecular kinetic energy, (c) root-mean-square speed, and (d) internal energy.arrow_forwardA thermally insulated ideal gas of volume V, and temperature T expands to another enclosure of volume V, through a porous plug. What is the change in the temperature of the gas? V, (b) T In V, V, (c) T In V, (d) T In V2 V, -V, (a) 0arrow_forwardThree moles of an argon gas are at a temperature of 305 K. Calculate the average kinetic energy per atom, the root-mean-square (rms) speed of atoms in the gas, and the internal energy of the gas. (a) the average kinetic energy per atom (in J) ? J (b) the root-mean-square (rms) speed (in m/s) of atoms in the gas ?m/s (c) the internal energy of the gas (in J) ?Jarrow_forward
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