MCEN 3012 THERMODYNAMICS Spring 2023 Homework #8 - Due: 3/19 by 11:59 pm Covering Chapters 6.10 – 7.3 in the book 1. Write out the following amended Honor Code for this homework assignment: “On my honor, as a University of Colorado Boulder student, I have neither given nor received unauthorized assistance on this homework assignment. I have neither posted problems from this assignment (in part or in whole) to Chegg or similar app nor accessed answers to these problems posted by someone else, both of which, I understand, would be a violation of the Honor Code.” Then sign your name. 2. Your grandparents return from their search for a new refrigerator. They bought a super fancy one because the freezer can reach an even lower temperature than -25°C, and your grandmother wants to keep her frozen bird collection at as low a temperature as possible. a) Using the diagram below, explain the freezer cycle to your grandparents starting with State 1 at the inlet to the compressor. You can use short, bulleted statements. Kitchen: 25°C -18 °C b) Draw the P-V diagram for this cycle, showing where heat and work enter and leave the system, i.e., the working fluid. Using this diagram, explain to your grandmother why it takes more energy to run the freezer at a lower temperature. MCEN 3012 THERMODYNAMICS Spring 2023 c) Using the COP for a Carnot refrigerator, explain why it takes more energy to run the freezer at a lower temperature. d) For a room temperature of 25°C, a coefficient of performance of 1.2, and 42 W to run the freezer, calculate the total rate of entropy change for the freezer, assuming that the total rate of entropy change for the freezer is the sum of the rate of entropy change for the hot and cold reservoirs. e) Calculate the total rate of entropy change for the freezer, for a fully reversible freezer running between the same two reservoirs and with the same power to run the freezer. Bonus question) Approximating the freezer as a Carnot refrigerator that has a working fluid that undergoes liquid-gas phase transitions, draw the T-S diagrams for this cycle, showing where heat and work enter and leave the working fluid. Using this diagram, explain why it takes more energy to run the freezer at a lower temperature. 3. Find the missing properties and the phase of the system. a) Find h, T, x for H2O s = 7.70 kJ/kg K, P = 25 kPa b) Find s, T, x for H2O u = 3400 kJ/kg, P = 10 MPa c) Find s, v for R-134a x = 0.45, T = -10°C 4. You see an ad in the Daily Camera for someone to tend to the Frozen Dead Guy in Nederland over the summer while his normal caretaker goes on vacation, and you decide to apply. You’re having a great summer climbing the 14ers with your new friends in Nederland. Your mom and dad decide to visit you for a few weeks. They suggest you go climb another peak while they do a little tidying up of your summer place. While you’re out, they decide that your crazy freezer really needs to be defrosted and cleaned. They take Grandpa Bredo out of the Mausoleum and put him on the grass in the shade. By the time they get him out of the Mausoleum and onto the grass, he is 0°C. The air temperature in the shade is a pleasant 22°C. a) Assuming that Grandpa Bredo is mostly water and weighs 65.5 kg, how much entropy is generated while Grandpa Bredo is fully thawed? Assume that the process starts after he is on the grass and ends before his temperature starts to increase. MCEN 3012 THERMODYNAMICS Spring 2023 b) When you get home, you find Grandpa Bredo on the grass. He’s fully thawed, but his body temperature is still 0°C. You quickly throw him in your bathtub with a bunch of dry ice. The sublimation temperature of dry ice is -78.4°C. How much entropy is generated in the process of fully freezing him again? c) How much entropy is generated over the cycle? d) Did we violate the second law of thermodynamics? Why or why not?
