College Physics
10th Edition
ISBN: 9781285737027
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Textbook Question
Chapter 12, Problem 28P
Suppose the Universe is considered to be an ideal gas of hydrogen atoms expanding adiabatically. (a) If the density of the gas in the Universe is one hydrogen atom per cubic meter, calculate the number of moles per unit volume (n/V). (b) Calculate the pressure of the Universe, taking the temperature of the Universe as 2.7 K. (c) If the current radius of the Universe is 15 billion light-years (1.4 × 1026 m), find the pressure of the Universe when it was the size of a nutshell, with radius 2.0 × 10−2 m. (Be careful: Calculator overflow can occur.)
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If one could somehow (pretend) get the temperature of an ideal gas to be absolute zero (i.e., 0 K) which of the following properties of the molecules of that gas would not be zero? (If you do not like pretending, for an ideal gas which of the following properties of the molecules does not have to be close to zero when the temperature is close to absolute zero?)
Group of answer choices
a) Average speed would not go to zero.
b) Average momentum would not go to zero.
c) Average kinetic energy would not go to zero.
d) More than one of these would not go to zero.
e) None of these (that is, they would all go to zero).
Consider two containers, one holding 1 kg of argon at 300 K and the other holding1 kg of krypton at 500 K. In each vessel, the average microscopic speed is given bȳv = √8kbT /πm
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?
Chapter 12 Solutions
College Physics
Ch. 12.1 - By visual inspection, order the PV diagrams shown...Ch. 12.4 - Three engines operate between reservoirs separated...Ch. 12.5 - Which of the following is true for the entropy...Ch. 12.5 - Prob. 12.5QQCh. 12 - Prob. 3CQCh. 12 - Prob. 4CQCh. 12 - For an ideal gas in an isothermal process, there...Ch. 12 - Is it possible to construct a heat engine that...Ch. 12 - When a sealed Thermos bottle full of hot coffee is...Ch. 12 - The first law of thermodynamics says we cant get...
Ch. 12 - Prob. 13CQCh. 12 - Prob. 14CQCh. 12 - An ideal gas is compressed to half its initial...Ch. 12 - A thermodynamic process occurs in which the...Ch. 12 - Prob. 17CQCh. 12 - An ideal gas is enclosed in a cylinder with a...Ch. 12 - Sketch a PV diagram and find the work done by the...Ch. 12 - Gas in a container is at a pressure of 1.5 atm and...Ch. 12 - A 40.0-g projectile is launched by the expansion...Ch. 12 - A gas expands from I to F along the three paths...Ch. 12 - Sketch a PV diagram of the following processes:...Ch. 12 - A sample of helium behaves as an ideal gas as it...Ch. 12 - (a) Find the work done by an ideal gas as it...Ch. 12 - One mole of an ideal gas initially at a...Ch. 12 - (a) Determine the work done on a fluid that...Ch. 12 - Prob. 11PCh. 12 - A cylinder of volume 0.300 m3 contains 10.0 mol of...Ch. 12 - A gas expands from I to F in Figure P12.5. The...Ch. 12 - In a running event, a sprinter does 4.8 105 J of...Ch. 12 - A gas is compressed at a constant pressure of...Ch. 12 - A quantity of a monatomic ideal gas undergoes a...Ch. 12 - A gas is enclosed in a container fitted with a...Ch. 12 - A monatomic ideal gas under-goes the thermodynamic...Ch. 12 - An ideal gas is compressed from a volume of Vi =...Ch. 12 - A system consisting of 0.025 6 moles of a diatomic...Ch. 12 - An ideal monatomic gas expands isothermally from...Ch. 12 - An ideal gas expands at constant pressure. (a)...Ch. 12 - An ideal monatomic gas is contained in a vessel of...Ch. 12 - Consider the cyclic process described by Figure...Ch. 12 - A 5.0-kg block of aluminum is heated from 20C to...Ch. 12 - One mole of gas initially at a pressure of 2.00...Ch. 12 - Consider the Universe to be an adiabatic expansion...Ch. 12 - Suppose the Universe is considered to be an ideal...Ch. 12 - A gas increases in pressure from 2.00 atm to 6.00...Ch. 12 - An ideal gas expands at a constant pressure of...Ch. 12 - A heat engine operates between a reservoir at 25C...Ch. 12 - A heat engine is being designed to have a Carnot...Ch. 12 - The work done by an engine equals one-fourth the...Ch. 12 - In each cycle of its operation, a heat engine...Ch. 12 - One of the most efficient engines ever built is a...Ch. 12 - A gun is a heat engine. In particular, it is an...Ch. 12 - An engine absorbs 1.70 kJ from a hot reservoir at...Ch. 12 - A heat pump has a coefficient of performance of...Ch. 12 - A freezer has a coefficient of performance of...Ch. 12 - Suppose an ideal (Carnot) heal pump could be...Ch. 12 - In one cycle a heat engine absorbs 500 J from a...Ch. 12 - A power plant has been proposed that would make...Ch. 12 - Prob. 43PCh. 12 - A heat engine operates in a Carnot cycle between...Ch. 12 - A Styrofoam cup holding 125 g of hot water at 1.00...Ch. 12 - A 65-g ice cube is initially at 0.0C. (a) Find the...Ch. 12 - A freezer is used to freeze 1.0 L of water...Ch. 12 - What is the change in entropy of 1.00 kg of liquid...Ch. 12 - A 70.0-kg log falls from a height of 25.0 m into a...Ch. 12 - Prob. 50PCh. 12 - Prob. 51PCh. 12 - When an aluminum bar is temporarily connected...Ch. 12 - Prepare a table like Table 12.3 for the following...Ch. 12 - Prob. 54PCh. 12 - Prob. 55PCh. 12 - Prob. 56PCh. 12 - Sweating is one of the main mechanisms with which...Ch. 12 - A Carnot engine operates between the temperatures...Ch. 12 - Prob. 59APCh. 12 - A Carnot engine operates between 100C and 20C. How...Ch. 12 - A substance undergoes the cyclic process shown in...Ch. 12 - When a gas follows path 123 on the PV diagram in...Ch. 12 - Prob. 63APCh. 12 - An ideal gas initially at pressure P0, volume V0,...Ch. 12 - One mole of neon gas is heated from 300. K to 420....Ch. 12 - Every second at Niagara Falls, approximately 5.00 ...Ch. 12 - A cylinder containing 10.0 moles of a monatomic...Ch. 12 - Prob. 68APCh. 12 - Suppose you spend 30.0 minutes on a stair-climbing...Ch. 12 - Hydrothermal vents deep on the ocean floor spout...Ch. 12 - An electrical power plant has an overall...Ch. 12 - A diatomic ideal gas expands from a volume of VA =...
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- prove average total kinetic energy = 2kT for gas molecules crossing a spherical area, with the following equations.arrow_forwardIn the hot gases of an automotive engine's cylinders, temperatures may exceed 3100 k. What would be the "root mean square" or "rms" velocity of a hydrogen atom, if one happened to be in that gas after some chemical reaction? The mass of a hydrogen atom is about 1.66x10-27 kg. Give your answer in m/s, but enter only the number.arrow_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_forward
- 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_forwardIn a certain particle accelerator, protons travel around a circular path of diameter 23.0 m in an evacuated chamber, whose residual gas is at 295 K and 1.00 * 10-6 torr pressure. (a) Calculate the number of gas molecules per cubic centimeter at this pressure. (b) What is the mean free path of the gas molecules if the molecular diameter is 2.00 * 10-8 cm?arrow_forwardIn an interstellar gas cloud at 50.0 K, the pressure is 1.00 * 10-8 Pa. Assuming that the molecular diameters of the gases in the cloud are all 20.0 nm, what is their mean free path?arrow_forward
- For hydrogen gas. H2, tables give values for the parameters of eqn 7a of a= 2728J K-1 mol-1, b=3.26 x 10-3 J K-2 mol-1, and c = 0.50 J K2 mol-1. Calculate the value of the constantpressure heat capacity of hydrogen at 25 °c.arrow_forwardIn 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.arrow_forwardDoes the temperature in the Clausius inequality relation have to be absolute temperature? Why?arrow_forward
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