A vertical cylinder of cross sectional area A is fitted with a tight-fitting, frictionless piston of mass m (figure below). Gas (a) If n moles of an ideal gas are in the cylinder at a temperature of T, use Newton's second law for equilibrium to show that the height h at which the piston is in equilibrium under its own weight is given by nRT h = mg + PA where P, is atmospheric pressure. (Submit a file with a maximum size of 1 MB.) Choose FileNo file chosen This answer has not been graded yet. (b) Is the pressure inside the cylinder less than, equal to, or greater than atmospheric pressure? O less than O equal to O greater than

A vertical cylinder of cross sectional area A is fitted with a tight-fitting, frictionless piston of mass m (figure below). Gas (a) If n moles of an ideal gas are in the cylinder at a temperature of T, use Newton's second law for equilibrium to show that the height h at which the piston is in equilibrium under its own weight is given by nRT h = mg + PA where P, is atmospheric pressure. (Submit a file with a maximum size of 1 MB.) Choose FileNo file chosen This answer has not been graded yet. (b) Is the pressure inside the cylinder less than, equal to, or greater than atmospheric pressure? O less than O equal to O greater than

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter2: The Kinetic Theory Of Gases

Section: Chapter Questions

Problem 81AP: One process for decaffeinating coffee uses carbon dioxide ( M=44.0 g/mol) at a molar density of...

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Using a numerical integration method such as Simpson's rule, find the fraction of molecules in a sample of oxygen gas at a temperature of 250 K that have speeds between 100 m/s and 150 m/s. The molar mass of oxygen (O2) is 32.0 g/mol. A precision to two significant digits is enough.
What is the total translational kinetic energy of the air molecules in a room of volume 23 m3 if the pressure is 9.5104 Pa (the room is at fairly high elevation) and die temperature is 21 ? Is any item of data unnecessary for the solution?
For a temperature increase of 10 at constant volume, what is the heat absorbed by (a) 3.0 mol of a dilute monatomic gas; (b) 0.50 mol of a dilute diatomic gas; and (c) 15 mol of a dilute polyatomic gas?
One might think that the internal energy of diatomic gases is given by Eint=5RT/2 . Do diatomic gases near room temperature have more or less internal energy than that? Hint: Their internal energy includes the total energy added in raising the temperature from the boiling point (very low) to room temperature.
Under what circumstances would you expect a gas to behave significantly differently than predicted by the ideal gas law?
Two moles of a monatomic ideal gas at (5 MPa, 5 L) is expanded isothermally until the volume is doubled (step 1). Then it is cooled isochorically until the pressure is 1 MPa (step 2). The temperature drops in this process. The gas is now compressed isothermally until its volume is back to 5 L, but its pressure is now 2 MPa (step 3). Finally, the gas is heated isochorically to return to the initial state (step 4). (a) Draw the four pi-cresses in the pV plane. (b) Find the total work done by the gas.
One process for decaffeinating coffee uses carbon dioxide ( M=44.0 g/mol) at a molar density of about 14,0 mol/m3 and a temperature of about 60 . (a) Is CO2 a solid, liquid, gas, or supercritical fluid under those conditions? (b) The van der Waals constants for carbon dioxide are a=0.3658 Pa m6/mol2 and b=4.286105 m3/mol. Using the van der Waals equation, estimate pressure of CO2 at that temperature and density. `
A system consisting of 20.0 mol of a monoatomic ideal gas is cooled at constant pressure from a volume of 50.0 L to 10.0 L. The initial temperature was 300 K. What is the change in entropy of the gas?
From 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.
One of a dilute diatomic gas occupying a volume of 10.00 L expands against a constant pressure of 2.000 atm when it is slowly heated. If the temperature of the gas rises by 10.00 K and 400.0 J of heat are added in the process, what is its final volume?
In the text, we showed that if the Clausius statement is false, the Kelvin statement must also be false. Now show the reverse, such that if the Kelvin statement is false, it follows that Clausius statement is false.
An aluminum rod 0.500 m in length and with a cross-sectional area of 2.50 cm2 is inserted into a thermally insulated vessel containing liquid helium at 4.20 K. The rod is initially at 300 K. (a) If one-half of the rod is inserted into the helium, how many liters of helium boil off by the time the inserted half cools to 4.20 K? Assume the upper half does not yet cool. (b) If the circular surface of the upper end of the rod is maintained at 300 K, what is the approximate boil-off rate of liquid helium in liters per second after the lower half has reached 4.20 K? (Aluminum has thermal conductivity of 3 100 W/m K at 4.20 K; ignore its temperature variation. The density of liquid helium is 125 kg/m3.)