In the simple kinetic theory of a gas we discussed in class, the molecules are assumed to be point-like objects (without any volume) so that they rarely collide with one another. In reality, each molecule has a small volume and so there are collisions. Let's assume that a molecule is a hard sphere of radius r. Then the molecules will occasionally collide with each other. The average distance traveled between two successive collisions (called mean free path) is λ = V/(4π √2 r2N) where V is the volume of the gas containing N molecules. Calculate the mean free path of a H2 molecule in a hydrogen gas tank at STP. Assume the molecular radius to be 10-10 a) 2.1*10-7 m                                       b) 4.2*10-7 m                                  c) none of these.

Two cards are drawn from a shuffled deck. What is the probability that both are aces? If you know that at least one is an ace, what is the probability that both are aces? If you know that one is the ace of spades, what is the probability that both are aces?

Consider an ideal gas of N molecules, in equilibrium in a container of volume V . Calculatea. the probability p1 of finding all molecules concentrated in a volume V /3 (macrostate 1);b. the probability p2 of finding all molecules concentrated in a volume 2V /3 (macrostate 2);c. the probability p of finding N/3 of the molecules concentrated in a volume V / 3 and the othersin the remaining volume;d. the entropy difference ∆S = S2 - S1 between states 1 and 2;e. the numerical values of p1, p2, and p for N = 9.