5 Bath Entropy In order to relax during midterms, you decide to go take a hot bath. Unfortunately, your roommate has already used most of the hot water! You're able to fill the tub with 195 kg of warm water (at 30 "C), and because you've been studying for your thermo exam, you have the brilliant idea to add boiling water to the tub to warm it up further. (a) While you are boiling the water, 0.5 kg of the liquid boils off into steam. What is the change in entropy of the water due to the phase transition? (b) How much (by weight) hot water (post-boiling, at 100 "C) do you need to add to the tub to bring the final temperature to 37 .C? (c) What is the entropy change of the hot water during its cooling? What is the entropy change of the warm water when it heats up? What is the total change in entropy for the system of all the water? (d) You sit in the bathtub until the water cools to 27 "C. Assuming that all the heat given off by the water is absorbed into the air, and that the air doesn't significantly change in temperature, what is the change in entropy of the air during the bathwater's cooling? (Assume room temperature is 20 "C.)