(a) How many atoms of helium gas fill a spherical balloon of diameter 30.6 cm at 23.0°C and 1.00 atm?Enter a number lationship between pressure, volume and temperature for an ideal gas? atoms(b) What is the average kinetic energy of the helium atoms?(c) What is the ms speed of the helium atoms?km/s

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Answered: (a) How many atoms of helium gas fill a…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter16: Temperature And The Kinetic Theory Of Gases

Section: Chapter Questions

Problem 41P

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Using the approximation v1v1+v f(v)dvf(v1)v for small v , estimate the fraction of nitrogen molecules at a temperature of 3.00102 K that have speeds between 290 m/s and 291 m/s.
Fifteen identical particles have various speeds: one has a speed of 2.00 m/s, two have speeds of 3.00 m/s, three have speeds of 5.00 m/s, four have speeds of 7.00 m/s, three have speeds of 9.00 m/s, and two have speeds of 12.0 m/s. Find (a) the average speed, (b) the rms speed, and (c) the most probable speed of these particles.
A company advertises that it delivers helium at a gauge pressure of 1.72107 Pa in a cylinder of volume 43.8 L. How many balloons can be inflated to a volume of 4.00 L with that amount of helium? Assume the pressure inside the balloons is 1.72105 Pa and the temperature in the cylinder and the balloons is 25.0 .
Under what circumstances would you expect a gas to behave significantly differently than predicted by the ideal gas law?
Consider a cylinder with a movable piston containing n moles of an ideal gas. The entire apparatus is immersed in a constant temperature bath of temperature T kelvin. The piston is then pushed slowly so that pressure of the gas changes quasi-statically from p1 to p2 at constant temperature T. Find the work done by the gas in terms of n, R T, p1 , and p2 .
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 P20.29ANS
Two monatomic ideal gases A and B are at the same temperature. If 1.0 g of gas A has the same internal energy as 0.10 g of gas B, what are (a) the ratio of the number of moles of each gas and (b) the ration of the atomic masses of the two gases?
One cylinder contains helium gas and another contains krypton gas at the same temperature. Mark each of these statements true, false, or impossible to determine from the given information. (a) The rms speeds of atoms in the two gases are the same. (b) The average kinetic energies of atoms in the two gases are the same. (c) The internal energies of 1 mole of gas in each cylinder are the same. (d) The pressures in the two cylinders ale the same.
Eight bumper cars, each with a mass of 322 kg. are running in a room 21.0 m long and 130 m wide. They have no driver, so they just bounce around on their own. The rms speed of the cars is 2.50 m/s. Repeating the arguments of Pressure, Temperature, and RMS Speed, find the average force per unit length (analogous to Pressure) that the cars exert the walls.
An airtight dispenser for drinking water is 25 cm × 10 cm in horizontal dimensions and 20 cm tall. It has a tap of negligible volume that opens at the level of the bottom of the dispenser. Initially, it contains Water to a level 3.0 cm from the top and air at the ambient pressure, 1.00 atm, from there to the top. When the tap is opened, water will flow out until the gauge pressure at the bottom of dispenser, and thus at the opening of the tap, is 0. What volume of water flows out? Assume the temperature is constant, the dispenser is perfectly rigid, and the water has a constant density of 1000 kg/m3.
If you cool an ideal gas, such that the the absolute temperature of gas is reduced by half, then theaverage speed of the molecules that make up the gas will change by what factor?
A container with rigid walls holds n moles of a monatomic ideal gas. In terms of n, how many moles of the gas must be removed from the container to double the pressure while also doubling the rms speed of the gas atoms?

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