Download Thermodynamics I Exam 1: Problems and Solutions - Prof. Donald Siegel and more Exams Thermodynamics in PDF only on Docsity! ME235: Thermodynamics I Exam #1 February 16, 2012 7:00pm – 8:30pm SECTIONS 001 AND 002 Exam Rules Open Textbook One Page of Handwritten Notes and Calculator Allowed No Laptops or Cell Phones When you are done, staple your work pages to these sheets, with this cover page on top. Name: __________________________________ Problem 1 30 Points Problem 2 30 Points Problem 3 40 Points I have observed the honor code and neither given nor received aid on this exam. ____________________________________________ Signature Problem 1 (30 pts). A cylinder with cross-sectional area of 0.01 m 2 contains two copper pistons with masses mp1 = 5 kg and mp2 = 10 kg. Compartment A contains 2 m 3 of air at 100 o C, while Compartment B contains 3 m 3 of air at 100 o C. The external pressure P0 is 100 kPa. The air and copper are at the same temperature at all times. Heat is transferred to the system until its temperature is 150 o C. (a) Find the work done during the process. (b) Find the heat transfer during the process. Problem 2 (30 pts). A piston/cylinder made from 5 kg of aluminum contains 2 kg of saturated water vapor at 175 o C. The total external force restraining the piston is directly proportional to the cylinder volume cubed, and a set of stops constrains the maximum volume to 0.5 m 3 . The aluminum is the same temperature as the water at all times. The setup is now heated to 1000 o C. (a) Plot the process for the water on a P vs. v diagram, with the beginning and end of the process clearly labeled. Show any phase boundaries, and also label the axes with numerical values for P and v (including units) at the beginning and end of the process as well as any important intermediate points. Clearly justify the shape of the P-v curve for every step in the process, using quantitative reasoning. (b) Find the work done during the process. (c) Find the heat transfer during the process. Problem 3 (40 pts). A piston/cylinder system has two compartments (A and B) separated by a membrane. Compartment A contains 0.1 m 3 of air at 1500 kPa and 100 o C, while Compartment B contains 0.2 m 3 of air at 4000 kPa and 150 o C. The cylinder also contains a linear spring, which is initially in equilibrium (unstretched) and has a spring constant k of 15000 N/m. The cross-sectional area of the cylinder is 0.1 m 2 . The membrane slowly ruptures, and the air comes to a uniform state at 350 o C. (a) Find the work done during the process. Hint: to determine how high the piston rises, consider what the air temperature would have to be in order for the piston to reach the stops. (b) Find the heat transfer during the process. Fext 3 5 z [m] 0 7 A B A B mp1 mp2 P0
