Use the worked example above to help you solve this problem. A cylinder contains 2.15 mol of helium gas at 18.5°C. Assume that the helium behaves like an ideal gas. (a) Find the total internal energy of the system. J (b) What is the average kinetic energy per molecule? J (c) How much energy would have to be added to the system to double the rms speed? The molar mass of helium is 4.00 10-3 kg/mol.

Use the worked example above to help you solve this problem. A cylinder contains 2.15 mol of helium gas at 18.5°C. Assume that the helium behaves like an ideal gas. (a) Find the total internal energy of the system. J (b) What is the average kinetic energy per molecule? J (c) How much energy would have to be added to the system to double the rms speed? The molar mass of helium is 4.00 10-3 kg/mol.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter20: Kinetic Theory Of Gases

Section: Chapter Questions

Problem 27PQ

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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
3. 0.5 moles of cinnamaldehyde gas that has an initial volume of ten liters expands under the following conditions: 185°F and 800mmHg external pressure.a. How much work is done? Express your answer in L atm.b. Assuming that the container is cylindrical with a base radius of 10cm and can only expand vertically, how much kinetic energy does a single molecule possesses if it travels from base to base of the expanded cylinder in 10μs? Express your answer in J. (Note that 1L atm=101.325J)
3. 0.5 moles of cinnamaldehyde gas that has an initial volume of ten liters expands under the followingconditions: 185°F and 800mmHg external pressure.a. How much work is done? Express your answer in L atm.b. Assuming that the container is cylindrical with a base radius of 10cm and can only expandvertically, how much kinetic energy does a single molecule possesses if it travels from baseto base of the expanded cylinder in 10μs? Express your answer in J.
An ideal gas is kept in a container of constant volume. The pressure of the gas is also kept constant. (a) Ifthe number of molecules in the gas is doubled, does the rms speedincrease, decrease, or stay the same? Explain. (b) If the initial rmsspeed is 1300 m>s, what is the final rms speed?
‼️Illustrate the problem ONLY: A rubberized sphere contains carbon dioxide. If the initial radius of the sphere is 15cm: a. How much work is done if the carbon dioxide-filled sphere expanded to five times its original volume against the pressure at STP? Express your answer in L atm. b. Upon the expansion of the sphere, what is the kinetic energy of a single carbon dioxide molecule if it travels across the diameter and covers it in 30ms? Assume that the sphere contains one mole of carbon dioxide. Express your answer in J. b. How much power can all the molecules in this sphere generate after 30s? Assume that the sphere contains one mole of carbon dioxide and that all molecules have the same kinetic energy. Express your answer in W. (Use the KE obtained from the previous required)‼️Illustrate the problem ONLY
Let’s assume dry air behaves like an ideal gas and has a molar mass of 28.8 g/mol.a) What is the approximate density of dry air at sea level when the air temperature is 32°C? Hint: How is the unit of standard atmosphere (symbol atm) defined?b) Briefly show and/or explain why this assumption for the molar mass of dry air is reasonable.c) Briefly show and/or explain how the density of air would change with increasing humidity.
Boyles Law states that when a sample of gas is compressed at a constant temperature, the product of the pressure and the volume remains constant: PV=C. A. Find the rate of change of volume with respect to pressure. B. A sample of gas in a container at low pressure and is steadily compressed at constant temperature for 10 minutes. Is the volume decreasing more rapidly at the beginning or the end of the 10minutes? Please Explain.. C. Prove that the isothermal compressibility is given by B=1/P.
Hi, could I get some help with this micro-macro connection physics problem involving root mean square speed? The set up is: For an atom in an ideal gas with rms speed in one direction, vx = 100 m/s, and mass m = 6.66e-27 kg, what is the temperature T in kelvin (K) to four digits of precision if Boltzman constant kB = 1.38e-23 J/K? Thank you.
ILLUSTRATE THE PROBLEM ONLY!!! 5 moles of cinnamaldehyde gas that has an initial volume of ten liters expands under the following conditions: 185°F and 800mmHg external pressure. a. How much work is done? Express your answer in L atm. b. Assuming that the container is cylindrical with a base radius of 10cm and can only expand vertically, how much kinetic energy does a single molecule possesses if it travels from base to base of the expanded cylinder in 10μs? Express your answer in J. ILLUSTRATE THE PROBLEM ONLY!!!
Consider the two-sided chamber shown,where the right half has a volume of V = 490 L and the left half has a volume of 2V. The chamber has a seal which separates the right from the left half. The chamber is sealed and an ideal gas is pumped into the right side at a pressure P = 3.2 atm and temperature T = 72° C. The seal between the two sides is then opened. (A) If the physical temperature decreases by a factor of 2 while the gas fills the chamber, what is the new pressure, in kilopascals? (B)The chamber is then sealed again, trapping 2/3 of the gas molecules in the left side. The temperature of the left side is then doubled, back to the original temperature T. What is the pressure in the left side of the chamber now, in kilopascals?
Consider the two-sided chamber shown,where the right half has a volume of V = 490 L and the left half has a volume of 2V. The chamber has a seal which separates the right from the left half. The chamber is sealed and an ideal gas is pumped into the right side at a pressure P = 3.2 atm and temperature T = 72° C. The seal between the two sides is then opened. (A) If the physical temperature decreases by a factor of 2 while the gas fills the chamber, what is the new pressure, in kilopascals? (B) The chamber is then sealed again, trapping 2/3 of the gas molecules in the left side. The temperature of the left side is then doubled, back to the original temperature T. What is the pressure in the left side of the chamber now, in kilopascals?
The fpicture shows a pV diagram for an ideal gas in which its pressure tripled from a to b when 804 J of heat was put into the gas. a) How much work was done on or by the gas between aa and bb? Express your answer in joules. b) Fill in the sentence, do they increase, decrease, or stay the same. " The temperature of this gas ______ between a and b. When pressure increases, the temperature _____ provided that V and n are _______." c) By how much did the internal energy of the gas change between a and b? Express your answer in joules. Did it increase or decrease? d) What is the temperature of the gas at point b in terms of its temperature at a, Ta