A sample of neon gas has of thermal energy. Estimate the average speed of a neon atom.
The average spped of a neon atom is
The gravitational potential between atoms is 0 in the micro system, and the total energy of a monatomic gas equals translational kinetic energy.. As a result, a monatomic gas's thermal energy is atoms is given by equation in the form
Where is the average energy. The molecule with mass and velocity has a translational kinetic energy on average The average translational kinetic energy of a molecule is affected by its temperature, hence it is related to the temperature per molecule in the form.
Where is Boltzmann's constant and in unit its value is
Knowing the mass and the molar mass , we can get the number of molecules by
Use this expressions of and into equation (1) to get an expression for
(3) for and use the values for and
Uranium has two naturally occurring isotopes. has a natural abundance of and has an abundance of . It is the rarer that is needed for nuclear reactors. The isotopes are separated by forming uranium hexafluoride, , which is a gas, then allowing it to diffuse through a series of porous membranes. has a slightly larger rms speed than and diffuses slightly faster. Many repetitions of this procedure gradually separate the two isotopes. What is the ratio of the rms speed of to that of
Consider a container like that shown in Figure , with moles of a monatomic gas on one side and moles of a diatomic gas on the other. The monatomic gas has initial temperature . The diatomic gas has initial temperature . a. Show that the equilibrium thermal energies are
b. Show that the equilibrium temperature is
c. of helium at an initial temperature of interacts thermally with of oxygen at an initial temperature of . What is the final temperature? How much heat energy is transferred, and in which direction?
At what temperature does thespeed of a nitrogen molecule and a hydrogen molecule equal the escape speed from the earth's surface? You'll find that these temperatures are very high, so you might think that the earth's gravity could easily contain both gases. But not all molecules move with . There is a distribution of speeds, and a small percentage of molecules have speeds several times . Bit by bit, a gas can slowly leak out of the atmosphere as its fastest molecules escape. A reasonable rule of thumb is that the earth's gravity can contain a gas only if the average translational kinetic energy per molecule is less than of the kinetic energy needed to escape. Use this rule to show why the earth's atmosphere contains nitrogen but not hydrogen, even though hydrogen is the most abundant element in the universe.
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