University Physics with Modern Physics (14th Edition)
14th Edition
ISBN: 9780321973610
Author: Hugh D. Young, Roger A. Freedman
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 18, Problem 18.7DQ
The derivation of the ideal-gas equation included the assumption that the number of molecules is very large, so that we could compute the average force due to many collisions. However, the ideal-gas equation holds accurately only at low pressures, where the molecules are few and far between. Is this inconsistent? Why or why not?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
The derivation of the ideal-gas equation included the assumption that the number of molecules is very large, so that we could compute the average force due to many collisions. However, the ideal-gas equation holds accurately only at low pressures, where the molecules are few and far between. Is this inconsistent? Why or why not?
How many molecules are in a typical object, such as gas in a tire or water in a drink? We can use the ideal gas law to give us an idea of how large N typically is.Calculate the number of molecules in a cubic meter of gas at standard temperature and pressure (STP), which is defined to be 0ºC and atmospheric pressure.
In the simple kinetic theory of a gas we discussed in class, the molecules are assumed to be point-like objects (without any volume) so that they rarely collide with one another. In reality, each molecule has a small volume and so there are collisions. Let's assume that a molecule is a hard sphere of radius r. Then the molecules will occasionally collide with each other. The average distance traveled between two successive collisions (called mean free path) is λ = V/(4π √2 r2N) where V is the volume of the gas containing N molecules. Calculate the mean free path of a H2 molecule in a hydrogen gas tank at STP. Assume the molecular radius to be 10-10
a) 2.1*10-7 m
b) 4.2*10-7 m
c) none of these.
Chapter 18 Solutions
University Physics with Modern Physics (14th Edition)
Ch. 18.1 - Rank the following ideal gases in order from...Ch. 18.2 - Prob. 18.2TYUCh. 18.3 - Rank the following gases in order from (a) highest...Ch. 18.4 - A cylinder with a fixed volume contains hydrogen...Ch. 18.5 - A quantity of gas containing N molecules has a...Ch. 18.6 - The average atmospheric pressure on Mars is 6.0 ...Ch. 18 - Section 18.1 states that ordinarily, pressure,...Ch. 18 - In the ideal-gas equation, could an equivalent...Ch. 18 - When a car is driven some distance, the air...Ch. 18 - The coolant in an automobile radiator is kept at a...
Ch. 18 - Unwrapped food placed in a freezer experiences...Ch. 18 - A group of students drove from their university...Ch. 18 - The derivation of the ideal-gas equation included...Ch. 18 - A rigid, perfectly insulated container has a...Ch. 18 - (a) Which has more atoms: a kilogram of hydrogen...Ch. 18 - Use the concepts of the kinetic-molecular model to...Ch. 18 - The proportions of various gases in the earths...Ch. 18 - Comment on the following statement: When two gases...Ch. 18 - Prob. 18.13DQCh. 18 - The temperature of an ideal gas is directly...Ch. 18 - If the pressure of an ideal monatomic gas is...Ch. 18 - In deriving the ideal-gas equation from the...Ch. 18 - Imagine a special air filter placed in a window of...Ch. 18 - Prob. 18.18DQCh. 18 - Consider two specimens of ideal gas at the same...Ch. 18 - The temperature of an ideal monatomic gas is...Ch. 18 - Prob. 18.21DQCh. 18 - (a) If you apply the same amount of heat to 1.00...Ch. 18 - Prob. 18.23DQCh. 18 - In a gas that contains N molecules, is it accurate...Ch. 18 - The atmosphere of the planet Mars is 95.3% carbon...Ch. 18 - Prob. 18.26DQCh. 18 - Ice is slippery to walk on, and especially...Ch. 18 - Hydrothermal vents are openings in the ocean floor...Ch. 18 - The dark areas on the moons surface are called...Ch. 18 - In addition to the normal cooking directions...Ch. 18 - A 20.0-L tank contains 4.86 104 kg of helium at...Ch. 18 - Helium gas with a volume of 3.20 L, under a...Ch. 18 - A cylindrical tank has a tight-fitting piston that...Ch. 18 - A 3.00-L lank contains air at 3.00 atm and 20.0C....Ch. 18 - Planetary Atmospheres. (a) Calculate the density...Ch. 18 - You have several identical balloons. You...Ch. 18 - A Jaguar XK8 convertible has an eight-cylinder...Ch. 18 - A welder using a tank of volume 0.0750 m3 fills it...Ch. 18 - A large cylindrical tank contains 0.750 m3 of...Ch. 18 - An empty cylindrical canister 1.50 m long and 90.0...Ch. 18 - The gas inside a balloon will always have a...Ch. 18 - An ideal gas has a density of 1.33 106 g/cm3 at...Ch. 18 - If a certain amount of ideal gas occupies a volume...Ch. 18 - A diver observes a bubble of air rising from the...Ch. 18 - A metal tank with volume 3.10 L will burst if the...Ch. 18 - Three moles of an ideal gas are in a rigid cubical...Ch. 18 - With the assumptions of Example 18.4 (Section...Ch. 18 - With the assumption that the air temperature is a...Ch. 18 - (a) Calculate the mass of nitrogen present in a...Ch. 18 - At an altitude of 11,000 m (a typical cruising...Ch. 18 - Prob. 18.21ECh. 18 - Prob. 18.22ECh. 18 - Modern vacuum pumps make it easy to attain...Ch. 18 - The Lagoon Nebula (Fig. E18.24) is a cloud of...Ch. 18 - In a gas at standard conditions, what is the...Ch. 18 - How Close Together Are Gas Molecules? Consider an...Ch. 18 - (a) What is the total translational kinetic energy...Ch. 18 - A flask contains a mixture of neon (Ne), krypton...Ch. 18 - We have two equal-size boxes, A and B. Each box...Ch. 18 - A container with volume 1.64 L is initially...Ch. 18 - Prob. 18.31ECh. 18 - Martian Climate. The atmosphere of Mars is mostly...Ch. 18 - Prob. 18.33ECh. 18 - Calculate the mean free path of air molecules at...Ch. 18 - At what temperature is the root-mean-square speed...Ch. 18 - Prob. 18.36ECh. 18 - Prob. 18.37ECh. 18 - Perfectly rigid containers each hold n moles of...Ch. 18 - (a) Compute the specific heat at constant volume...Ch. 18 - Prob. 18.40ECh. 18 - Prob. 18.41ECh. 18 - For a gas of nitrogen molecules (N2), what must...Ch. 18 - Prob. 18.43ECh. 18 - Meteorology. The vapor pressure is the pressure of...Ch. 18 - Calculate the volume of 1.00 mol of liquid water...Ch. 18 - A physics lecture room at 1.00 atm and 27.0C has a...Ch. 18 - CP BIO The Effect of Altitude on the Lungs. (a)...Ch. 18 - CP BIO The Bends. If deep-sea divers rise to the...Ch. 18 - CP A hot-air balloon stays aloft because hot air...Ch. 18 - In an evacuated enclosure, a vertical cylindrical...Ch. 18 - A cylinder 1.00 m tall with inside diameter 0.120...Ch. 18 - CP During a test dive in 1939, prior to being...Ch. 18 - Atmosphere or Titan. Titan, the largest satellite...Ch. 18 - Pressure on Venus. At the surface of Venus the...Ch. 18 - An automobile tire has a volume of 0.0150 m3 on a...Ch. 18 - A flask with a volume of 1.50 L, provided with a...Ch. 18 - CP A balloon of volume 750 m3 is to be filled with...Ch. 18 - A vertical cylindrical tank contains 1.80 mol of...Ch. 18 - CP A large tank of water has a hose connected to...Ch. 18 - CP A light, plastic sphere with mass m = 9.00 g...Ch. 18 - Prob. 18.61PCh. 18 - BIO A person at rest inhales 0.50 L of air with...Ch. 18 - You have two identical containers, one containing...Ch. 18 - The size of an oxygen molecule is about 2.0 1010...Ch. 18 - A sealed box contains a monatomic ideal gas. The...Ch. 18 - Helium gas is in a cylinder that has rigid walls....Ch. 18 - You blow up a spherical balloon to a diameter of...Ch. 18 - CP (a) Compute the increase in gravitational...Ch. 18 - Prob. 18.69PCh. 18 - Prob. 18.70PCh. 18 - It is possible to make crystalline solids that are...Ch. 18 - Hydrogen on the Sun. The surface of the sun has a...Ch. 18 - Prob. 18.73PCh. 18 - Planetary Atmospheres. (a) The temperature near...Ch. 18 - Prob. 18.75PCh. 18 - Prob. 18.76PCh. 18 - CALC (a) Explain why in a gas of N molecules, the...Ch. 18 - Prob. 18.78PCh. 18 - CP Oscillations of a Piston. A vertical cylinder...Ch. 18 - Prob. 18.80PCh. 18 - DATA The Dew Point and Clouds. The vapor pressure...Ch. 18 - DATA The statistical quantities average value and...Ch. 18 - CP Dark Nebulae and the Interstellar Medium. The...Ch. 18 - CALC Earths Atmosphere. In t he troposphere, the...Ch. 18 - Prob. 18.85PPCh. 18 - Estimate the ratio of the thermal conductivity of...Ch. 18 - The rate of effusionthat is, leakage of a gas...
Additional Science Textbook Solutions
Find more solutions based on key concepts
41. A 0.300 kg oscillator has a speed of 95.4cm/s when its displacement is 3.00cm and 71.4 cm/s when its displ...
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
32. (II) A merry-go-round accelerates from rest to 0.68 rad/s in 34 s. Assuming the merry-go-round is a uniform...
Physics: Principles with Applications
Give an example of a process in which no heat is added to a system, but its temperature increases. Then give an...
An Introduction to Thermal Physics
108 kg. The tower sways back and forth at a frequency of about 0.10Hz. (a) Estimate the effective spring consta...
College Physics
3. What is free-fall, and why does it make you weightless? Briefly describe why astronauts are weightless in th...
The Cosmic Perspective
If acceleration is proportional to the net force or is equal to net force.
Conceptual Physics (12th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- 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_forwardConsider a container filled with helium gas at room temperature and ambient pressure. (a) Sketch a graph of the distribution of molecular speeds in the container. (b) On the same graph, sketch the distribution for the same container at a lower temperature, clearly labelling the new curve.arrow_forwardProvide an equation of state (relating pressure, volume and temperature) for a real gas and interpret the terms that take into account the differences between a real and ideal gas. Comment on the extreme limits (example:zero temperature). Under what conditions does the behavior of real gases conform to the behavior expected to ideal gases?arrow_forward
- One mole of an ideal gas at standard temperature and pressure occupies 22.4 L (molar volume). What is the ratio of molar volume to the atomic volume of a mole of hydrogen ? (Take the size of hydrogen molecule to be about 1 Å). Why is this ratio so large ?arrow_forwardIn deriving the ideal-gas equation from the kinetic-molecular model, we ignored potential energy due to the earth' gravity. Is this omission justified? Why or why not?arrow_forwardThe temperature of an ideal monatomic gas is increased from 25C to 50C. Does the average translational kinetic energy of each gas atom double? Explain. If your answer is no, what would the final temperature be if the average translational kinetic energy was doubled?arrow_forward
- Consider 1 mole of a van der Waals gas. (i) Derive the expressions for the pressure, pc, temperature, Tc, and volume, Vc, in the critical point of a van der Waals gas in terms of parameters a, b and R. Derive the vdw equation in reduced coordinates p =,= 7, V = V/ (ii) (iii) Find how many times the gas temperature exceeds its critical temperature if the gas pressure is 4 times as high as critical pressure and the volume of gas is equal to twice the critical volume.arrow_forwardIf the pressure of an ideal monatomic gas is increased while the number of moles is kept constant, what happens to the average translational kinetic energy of one atom of the gas? Is it possible to change both the volume and the pressure of an ideal gas and keep the average translational kinetic energy of the atoms constant? Explain.arrow_forwardBy considering momentum changes for an individual molecule inside a rectangular box, derive an expression for PV in terms of molecular mass, the number of molecules, and mean square speed. Compare this to the ideal gas equation to show that the mean kinetic energy of a molecule is 1.5 kBarrow_forward
- So each four dot shows four different states for an ideal gas. P is the pressure and the other one is the density of the gas. Is temperature of state 1 less or greater than the state 2? Can you please explain why?arrow_forwardA container encloses 2 mol of an ideal gas that has molar mass M1 and 0.5 mol of a second ideal gas that has molar mass M2 = 3M1. What fraction of the total pressure on the container wall is attributable to the second gas? (The kinetic theory explanation of pressure leads to the experimentally discovered law of partial pressures for a mixture of gases that do not react chemically: The total pressure exerted by the mixture is equal to the sum of the pressures that the several gases would exert separately if each were to occupy the vessel alone. The molecule–vessel collisions of one type would not be altered by the presence of another type.)arrow_forwardThe equipartition theorem states that each term in the particle's energy depending on a squared position (potential energies) or velocity (kinetic energies) contributes on average kT to the particle's total mechanical energy. Each of these terms corresponds to a degree of freedom of the gas. That is, 6. By what factor do you have to increase the temperature to triple the rms speed of an ideal gas?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningModern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
The Laws of Thermodynamics, Entropy, and Gibbs Free Energy; Author: Professor Dave Explains;https://www.youtube.com/watch?v=8N1BxHgsoOw;License: Standard YouTube License, CC-BY