Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 20, Problem 14PQ
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The correct statement about the concept of temperature.
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Two containers hold ideal gases at the same temperature.Container A has twice the volume and half the number of molecules as container B. What is the ratio PA>PB, where PA is the pressure in container A and PB is the pressure in container B?
P1. Consider a gas of oxygen atoms (H0, = 32 g/mol). What should the temperature of
the gas be for the mean square speed of the atoms to be v = 100 m/s? While keeping the
temperature the same as before, what should the pressure of the gas be for a container of
volume V = 51 to be able to contain m = 1 kg of oxygen? How much does the temperature
of the gas increase if the container is dropped on the ground at a speed of u = 2 m/s? You
may neglect thermal conduction with the outside.
There are lots of examples of ideal gases in the universe, and they exist in many different conditions. In this problem we will examine what the temperature of these various phenomena are.
a. Give an expression for the temperature of an ideal gas in terms of pressure P, particle density per unit volume ρ, and fundamental constants.
b. Near the surface of Venus, its atmosphere has a pressure fv= 95 times the pressure of Earth's atmosphere, and a particle density of around ρv = 1.1 × 1027 m-3. What is the temperature of Venus' atmosphere (in C) near the surface?
c. The Orion nebula is one of the brightest diffuse nebulae in the sky (look for it in the winter, just below the three bright stars in Orion's belt). It is a very complicated mess of gas, dust, young star systems, and brown dwarfs, but let's estimate its temperature if we assume it is a uniform ideal gas. Assume it is a sphere of radius r = 4.7 × 1015 m (around 6 light years) with a total mass 4000 times the mass of the…
Chapter 20 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 20.2 - In Example 20.1, we found that the rms value of a...Ch. 20.3 - If the temperature of a gas is doubled, what...Ch. 20.3 - Prob. 20.3CECh. 20.5 - Prob. 20.4CECh. 20.7 - Prob. 20.5CECh. 20.8 - Prob. 20.6CECh. 20 - Prob. 1PQCh. 20 - Prob. 2PQCh. 20 - Prob. 3PQCh. 20 - Prob. 4PQ
Ch. 20 - Prob. 5PQCh. 20 - Prob. 6PQCh. 20 - Prob. 7PQCh. 20 - Prob. 8PQCh. 20 - Particles in an ideal gas of molecular oxygen (O2)...Ch. 20 - Prob. 10PQCh. 20 - Prob. 11PQCh. 20 - Prob. 12PQCh. 20 - Prob. 13PQCh. 20 - Prob. 14PQCh. 20 - The mass of a single hydrogen molecule is...Ch. 20 - Prob. 16PQCh. 20 - The noble gases neon (atomic mass 20.1797 u) and...Ch. 20 - Prob. 18PQCh. 20 - Prob. 19PQCh. 20 - Prob. 20PQCh. 20 - Prob. 22PQCh. 20 - Prob. 23PQCh. 20 - Prob. 24PQCh. 20 - Prob. 25PQCh. 20 - Prob. 26PQCh. 20 - Prob. 27PQCh. 20 - Prob. 28PQCh. 20 - Consider the Maxwell-Boltzmann distribution...Ch. 20 - Prob. 30PQCh. 20 - Prob. 31PQCh. 20 - Prob. 32PQCh. 20 - Prob. 33PQCh. 20 - Prob. 34PQCh. 20 - Prob. 35PQCh. 20 - Prob. 36PQCh. 20 - Prob. 37PQCh. 20 - Prob. 38PQCh. 20 - Prob. 39PQCh. 20 - Prob. 40PQCh. 20 - Prob. 41PQCh. 20 - Prob. 42PQCh. 20 - Prob. 43PQCh. 20 - Prob. 44PQCh. 20 - Figure P20.45 shows a phase diagram of carbon...Ch. 20 - Prob. 46PQCh. 20 - Prob. 47PQCh. 20 - Consider water at 0C and initially at some...Ch. 20 - Prob. 49PQCh. 20 - Prob. 50PQCh. 20 - Prob. 51PQCh. 20 - Prob. 52PQCh. 20 - Prob. 53PQCh. 20 - Prob. 54PQCh. 20 - Prob. 55PQCh. 20 - Prob. 56PQCh. 20 - Consider again the box and particles with the...Ch. 20 - Prob. 58PQCh. 20 - The average kinetic energy of an argon atom in a...Ch. 20 - For the exam scores given in Table P20.60, find...Ch. 20 - Prob. 61PQCh. 20 - Prob. 62PQCh. 20 - Prob. 63PQCh. 20 - Prob. 64PQCh. 20 - Prob. 65PQCh. 20 - Prob. 66PQCh. 20 - Determine the rms speed of an atom in a helium...Ch. 20 - Consider a gas filling two connected chambers that...Ch. 20 - Prob. 69PQCh. 20 - Prob. 70PQCh. 20 - A 0.500-m3 container holding 3.00 mol of ozone...Ch. 20 - Prob. 72PQCh. 20 - Prob. 73PQ
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- An ideal gas is contained in a vessel at 300 K. The temperature of the gas is then increased to 900 K. (i) By what factor does the average kinetic energy of the molecules change, (a) a factor of 9, (b) a factor of 3, (c) a factor of 3, (d) a factor of 1, or (e) a factor of 13? Using the same choices as in part (i), by what factor does each of the following change: (ii) the rms molecular speed of the molecules, (iii) the average momentum change that one molecule undergoes in a collision with one particular wall, (iv) the rate of collisions of molecules with walls, and (v) the pressure of the gas?arrow_forward(a) In the deep space between galaxies, me density of atoms is as low as 106atoms/m3, and me temperature is a frigid 2.7 K. What is me pressure? (b) What volume (in m3) is occupied by 1 mol of gas? (c) If this volume is a cube, what is the length of its sides in kilometers?arrow_forwardDetermine the rms speed of an atom in a helium balloon at standard temperature and pressure (T = 273.15 K and P = 1.00 105 Pa). Is it lower or higher than the rms speed of a nitrogen molecule in the atmosphere?arrow_forward
- (a) How many atoms of helium gas fill a spherical balloon of diameter 30.0 cm at 20.0C and 1.00 atm? (b) What is the average kinetic energy of the helium atoms? (c) What is the rms speed of the helium atoms?arrow_forwardConsider a gas filling two connected chambers that are separated by a removable barrier (Fig. P20.68). The gas molecules on the left (red) are initially at a higher temperature than the ones on the right (blue). When the barrier between the two chambers is removed, the molecules begin to mix and move from one chamber to the other. a. Describe what happens to the temperature in the left chamber and in the right chamber as time goes on, once the barrier is open. Discuss in terms of the mixing of the molecules from each gas. b. Describe what happens to the most probable speed and average speed in the left chamber and in the right chamber as time goes on, once the barrier is open. Do they increase or decrease by the same factor? Explain. FIGURE P20.68 Problems 68 and 69.arrow_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
- Five bicyclists are riding at the following speeds: 5.4 m/s, 5.7 m/s, 5.8 m/s, 6.0 m/s, and 6.5 m/s. (a) What is their average speed? (b) What is their rms speed?arrow_forwardA cylinder contains a mixture of helium and argon gas in equilibrium at 150C. (a) What is the average kinetic energy for each type of gas molecule? (b) What is the rms speed of each type of molecule?arrow_forwardThe number density in a container of neon gas is 5.40 x 1025 m³. The atoms are moving with an rms speed of 665 m/s. What is the pressure inside the container? Express your answer with the appropriate units. ► View Available Hint(s) p= Submit Part B Value T = μA Submit What is the temperature inside the container? Express your answer with the appropriate units. ► View Available Hint(s) μÀ Value Units 6 B Units ? px ?arrow_forward
- B. i. State the assumption of the kinetic theory of a gas that addresses molecular movement. ii. Given that: 3/2 kT = ½ m, where T = molecular temperature in kelvin and = molecular mean-square speed, sketch a general graph of T versus molecular root means square speed (c²>). jii. Given that for an ideal gas: PV = nRT, sketch a general graph of P versus T.arrow_forwardA cylinder in a car engine takes V1 = 0.045 m3 of air into the chamber at 300 C and at 1 atm pressure. The piston then compresses the air to one-ninth (V1/9) of the original volume and to 20 times (20 P1 ). A. What would be the new temperature if the pressure was constant?arrow_forwardAt very low temperatures, molecular speeds can still be large. The table below shows mass and temperature data for three different gases. The specified temperatures are each one degree above the boiling point for the substance. Part (a) What is the rms speed. in meters per second, for atoms of helium gas at the temperature specified in the table? Part (b) What is the ratio of the rms speed of the hydrogen molecules to that of the oxygen molecules? (Calculate each at its respective temperature from the table.)arrow_forward
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