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From what height must an oxygen molecule fall in a vacuum so that its kinetic energy at the bottom equals the average energy of an oxygen molecule at 300K?

Short Answer

Expert verified

The height of Oxygen molecule falls in a vacuum ofh=12×103m.

Step by step solution

01

Step: 1 Find Kinetic energy for oxygen molecule:

The average translational kinetic energy of a molecule with mass and velocity Vis The average translational kinetic energy of a molecule is affected by its temperature, hence it is related to the temperatureT per molecule in the manner

ϵavg=32kBT

Where kBis Boltzmann's constant and in SI unit its value is

kB=1.38×1023J/K

This average energy is equal to the kinetic energy of the oxygen molecule. Plug the values for kBand Tinto equation to get the kinetic energy for oxygen molecule

K=32kBT=321.38×1023J/K(300K)=6.2×1021J.

02

Step: 2 Finding height:

From the conservation law of energy, the potential energy Uof the molecule converts to the kinetic energy, so we can get the height hwhere the oxygen molecule fall by

U=KMgh=Kh=KMg.

03

Step: 3 The molecular mass 

The molecular mass of oxygen is m=16u. But oxygen is a diatomic gas, so the molecular mass of one molecule is m=32. Converting this to kg, we get the mass of one molecule of oxygen b M=32u×1.66×1027kg1u=53×1027kg

h=KMg

=6.2×1021J53×1027kg9.8m/s2

=12×103m

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Most popular questions from this chapter

The atmosphere of the sun consists mostly of hydrogen atoms (not molecules) at a temperature of 6000k. What are (a) the average translational kinetic energy per atom and (b) the rms speed of the atoms?

The pressure inside a tank of neon is 150atm. The temperature is 25°C. On average, how many atomic diameters does a neon atom move between collisions?

In the discussion following Equation 20.43 it was said that Q1=-Q2. Prove that this is so.

a. Find an expression for thevrmsof gas molecules in terms ofp,Vand the total mass of the gas M.

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c. A cylindrical sample chamber has a piston moving outward at 0.50m/sduring an isobaric expansion. The rms speed of the gas molecules is localid="1648640672000" 450m/sat the instant the chamber length is localid="1648640676590" 1.5m. At what rate is localid="1648640708264" vrmschanging?

Consider a container like that shown in Figure 20.12, with n1moles of a monatomic gas on one side and n2moles of a diatomic gas on the other. The monatomic gas has initial temperature T1i. The diatomic gas has initial temperatureT2i .
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E1f=3n13n1+5n2E1i+E2iE2f=5n23n1+5n2E1i+E2i

b. Show that the equilibrium temperature is

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c.2.0g of helium at an initial temperature of role="math" localid="1648474536876" 300Kinteracts thermally with 8.0gof oxygen at an initial temperature of600K . What is the final temperature? How much heat energy is transferred, and in which direction?

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