A. Consider a monatomic gas of particles each with mass m. What is vrms = sqrt(v^2), the root mean square (rms) of the x component of velocity of the gas particles if the gas is at an absolute temperature T?
B. Now consider the same system--a monatomic gas of particles of mass m --except in three dimensions. Find vrms, the rms speed if the gas is at an absolute temperature T.
C. What is the rms speed v0 of molecules in air at 0*C? Air is composed mostly of N2 molecules, so you may assume that it has molecules of average atomic mass 28.0 * 1.661 * 10^-26 kg. Neglect the rotation of the molecules for this part of the question.
D. Find sqert(w^2), the rms angular speed of the dumbbell about a single axis (taken to be the x axis), assuming that the dumbbell is lined up on the z axis and is in equilibrium at temperature T.
E. What is the typical rotational frequency f(rot) for a molecule like N2 at room temperature (25*C)? Assume that d for this molecule is 2 A = 2 * 10^-10 m. Take the atomic mass of N2 to be mN2 = 4.65 * 10^-26 kg. You will need to account for rotations around two axes (not just one) to find the correct frequency. The angular velocities add like vectors, so w^2 = (wx)^2 + (wy)^2 They have units of radians/sec.