Watch this short video on entropy by "Professor Dave." Entropy is a deep subject and a fundamental governing principle in the evolution of systems of objects. You may have heard entropy defined something along the lines of "a system always tends toward disorder" or similar, but this doesn't quite capture the full idea. After watching the video, answer the questions below. 1. (3 points) What is meant by a "reversible process"? 2. (3 points) What happens to the entropy of the universe for any process? 3. Consider a set of two dice: one red, one blue. Any configuration of the two dice is known as a microstate, while we reserve the term macrostate to refer to some quantity which denotes the combination of dice as a whole. I'll use the notation {r, b} to refer to a microstate of the red and blue dice system, where r refers to the face of the red die, and b refers to the face of the blue die after a toss. For example, consider the macrostate of "the two dice add up to 2." There is only one microstate that corresponds to this macrostate, namely {1, 1}, where both the red and blue dice have a face of 1 pointing up. The macrostate of "the two dice add up to 3" corresponds to two microstates, namely {1, 2} and {2, 1} (red: 1, blue: 2 and red: 2, blue: 1). The entropy of the two-dice system is proportional to the number of macrostates accessible by the system. (a) (3 points) How many microstates are there corresponding to the macrostate "the two dice add up to 4"? List them out and just count them up. (b) (3 points) How many microstates are there corresponding to the macrostate "the two dice add up to 6"? (c) (3 points) How many microstates are there corresponding to the macrostate "the red die is odd and the blue die is 6"? (d) (5 points) The likelihood of rolling a particular macrostate is proportional to the number of microstates accessible to the system. Macrostates with more microstate configurations have higher entropy. Which macrostate has higher entropy: A: "both dice have the same face" or B: "both dice add up to an even number"? https://www.youtube.com/watch?v=MrwW4w2nAMc