Kinetic theory and molecular speeds · BPhO 2008 #9
Physics · thermodynamics
Problem
A gas consists of particles moving around in random directions. Air molecules move with an average speed of 500 m/s at room temperature. In a balloon filled with hydrogen gas at the same room temperature, the hydrogen molecules would have the same average kinetic energy as the air molecules.
average relative molecular mass of air molecule = 29
relative molecular mass of hydrogen molecule = 2.0
a) Calculate the average speed of a hydrogen molecule. [3]
b) What is the average velocity of the hydrogen molecules in the balloon? [1]
c) Comment on how the speed of sound in hydrogen would compare with the speed of sound in air at the same temperature? [2]
d) If the mass of all the molecules of the hydrogen gas in the balloon is 1.0 g, calculate the sum of the kinetic energies of all the molecules in the balloon. [1]
e) If a balloon was filled with an identical number of air molecules at the same temperature, how would the sum of the kinetic energies of the air molecules compare with the value calculated in part (d) for hydrogen? [1]
f) If one of the hydrogen molecules was directed upwards from the surface of a planet which had no atmosphere, but was similar in size and mass to the earth and had the same gravitational field strength, to what height would the molecule go? (assume that g is independent of height) [2]
g) How does this height, calculated in part (f), compare with the height reached by an air molecule directed upwards from the planet in an identical manner? (A numerical answer is not required) [1]
h) This height is not enough to get away from the earth's gravitational pull, and yet the hydrogen molecules at the top of the atmosphere do escape completely from the earth's gravitational field. Explain how this could be so. [2]