Question: Assume you can prove that for our simple atomic model of an ideal gas the pressure P = 1/3 ρ2 , where ρ is the density of the gas and 2, is the average of the square of the velocity of the gas molecules.
a. Use the ideal gas law to derive a relation between the temperature of this gas (measured in kelvins) and the average kinetic energy of a gas molecule.
b. If the gas is helium (M = 4u), what is the value of the average kinetic energy of a helium atom at room temperature?
c. If the gas consisted of oxygen molecules (M = 32), what would be the average kinetic energy of a molecule at room temperature? Explain your answer.