Problem 1: One million pennies lie flat on a large table. a: In how many ways can one obtain a macrostate in which there are exactly 500 000 heads and an equal number of tails? b: What is the probability after 1 million coin tosses with a fair coin to get exactly 500 000 heads? c: What is the entropy (in units of the Boltzmann constant) of the state with 500 000 heads and an equal number of tails. Problem 2: An Einstein solid has on the average 1 vibrational quantum excited a: What is the entropy per oscillator? per oscillator. b: What is the temperature? Give your answer in units of the Einstein temperature TE = hw k Problem 3:Two Einstein solids have the same total number of oscillators. One solid has on the average one half vibrational quantum excited per oscillator the other has two. a: What are the temperatures of the two solids? Give your answer in units of the Einstein temperature b: What is the temperature if the two solids are joined and brought to thermal equilibrium?