# ps12sol - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01T Fall Term 2004 Problem Set 12: Kinetic Theory; Mechanical Equivalent of Heat Solutions Problem 1: Isothermal Ideal Gas Atmosphere a) Find the root mean square (rms) speed of an oxygen molecule at T = 300K at sea level. b) Find the root mean square z-component of the velocity of an oxygen molecule at T = 300K at sea level. c) If a molecule with the above z-velocity were in a large evacuated container, to what maximum height H would it rise? d) Find the rms z-component of velocity of a nitrogen molecule at T = 300K and height H assuming that the atmosphere extends that high (which it does)?

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Problem 2: Measuring Speeds of Gas Molecules The actual speeds of atoms and molecules were first measured directly in 1930 by the following experiment. A beam of bismuth atoms, evaporated from an ‘oven’, passed through some defining slits in a hollow cylinder of 2 radius R = 4.7 × 10 2 m , rotating with frequency f = 1.2 × 10 Hz . The cylinder had a narrow slit cut in one side parallel to its axis. A glass plate was mounted opposite the slit in the cylinder. (See sketch). The fastest atoms would arrive at the leading edge of the plate and the slower atoms would distribute themselves further back along the plate. The following graph shows the results for Bismuth atoms at a temperature T = 827 0 C . In this problem we shall calculate the velocity of the Bismuth atoms at the maximum of the distribution curve. The Bismuth atoms have a molecular weight M = 2.09 × 10 2 g mole . a) What is the displacement backwards along the glass of the maximum of the curve? b) What angle (in radians) does this correspond to?

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ps12sol - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department...

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