Kinetic Theory

Problem:

A 5-liter vessel contains 0.125 moles of an ideal gas at a pressure of 1.5 atm.  What is the average translational kinetic energy of a single molecule?

Solution:

Problem:

A cylinder contains a mixture of helium and argon gas in equilibrium at 150 oC.
(a)  What is the average kinetic energy of each gas molecule?
(b)  What is the root-mean-square speed of each type of molecule?
mHe = 4 u, mAr = 39.9 u.
1 u = 1 atomic mass unit = 1.66*10-27 kg.

Solution:

Problem:

(a)  For a gas of electrons in which quantum mechanical effects can be neglected, above what temperature would you expect special relativistic effects to become important?
(b)  For a gas of non-relativistic electrons, above what electron number density would you expect quantum mechanical behavior of the gas to become important if its temperature is 107 K?

Solution:

Problem:

An apparent limit on the lowest temperature achievable by laser cooling is reached when an atom's recoil energy upon absorbing or emitting a single photon is approximately equal to its total kinetic energy (3/2 kT).  Calculate this “recoil temperature” for the Rubidium atom.
(m = 85 u, u = 1.66 * 10-27kg) if the wavelength of the photon in resonance with Rubidium is 780 nm.

Solution:

Problem:

What is the root-mean-square speed of a thermal (room temperature) neutron?  Can you outrun it? (Show work!)

Solution: