Quiz 2 Practice Problems - Thermodynamics and Statistical Mechanics | PHYS 4420, Quizzes of Physics

Download Quiz 2 Practice Problems - Thermodynamics and Statistical Mechanics | PHYS 4420 and more Quizzes Physics in PDF only on Docsity! 1 PHYS-4420 THERMODYNAMICS & STATISTICAL MECHANICS SPRING 2003 Quiz 2 Friday, April 18, 2003 NAME: ____________________________________________ To receive credit for a problem, you must show your work, or explain how you arrived at your answer. 1. (15%) The Helmholtz Free Energy is defined as F = E – TS, where E is internal energy, T is temperature, and S is entropy. For a system where dW = pdV, show that NV T F S ,       , where N is the number of particles in the system. 2. (40%) One mole of an ideal monatomic gas traverses the idealized Diesel cycle shown in the figure. Process 12 is adiabatic, and process 23 takes place at constant pressure. Process 34 is also adiabatic, and process 41 takes place at constant volume. (Hint: for one mole of an ideal monatomic gas, the internal energy is RTE 2 3 .) The temperatures of the gas at points 1, 2, 3, and 4 are: T1 = 300 K, T2 = 1600 K, T3 = 1800 K, T4 = 365 K 2 a) (10%) Find V1/V2, the ratio of the volume of the gas at point 1 to the volume at point 2. (This is the compression ratio for the Diesel cycle.) V1/V2 = _____________ b) (10%) Find the magnitude of the heat added to the gas in the process 23. Express the answer in terms of the gas constant R. Q1 = _____________ c) (5%) Find the magnitude of the work done by the gas in the process 23. Express the answer in terms of the gas constant R. W23 = _____________ d) (5%) Find the magnitude of the heat removed from gas in the process 41. Express the answer in terms of the gas constant R. Q2 = _____________ e) (5%) How much work is done by the gas in one complete cycle? Express the answer in terms of the gas constant R. W = _____________