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Fa08-MT1-SunRev2-Soln

Fa08-MT1-SunRev2-Soln - Practice Midterm 1 Solution Please...

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Practice Midterm 1 Solution: Please e-mail Aritoki Suzuki ([email protected]) for questions. 1 Diesel Engine in P V A B C D T H L T Q out Q Figure 1: Diesel Engine a) Which point has highest/lowest temperature? As you can see on Figure 1, Point B is on the isotherm curve associated with T H . Point D is on the isotherm curve of T L . b) Find pressure and volume at B , C , and D using P A , V A , V H , V L and con- stants R We will solve this in order B D C . From P-V diagram, P B = P A (1) P B V B = nRT B (2) Replace T B = T L , P B = P A , and n = 1 P A V B = RT L (3) 1
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Solve for V B V B = RT L P A (4) To find P D , nR = P D V D T D (5) R = P D V D T L (6) Since process A D is adiabatic process P A V γ A = P D V γ D where γ = 7 5 R = P D V D T L (7) R = P 1 - 1 γ D P 1 γ A V A T L (8) Solving for P D yields P D = RT L V A P 1 γ A γ γ - 1 (9) To find V D , nR = P D V D T D (10) R = P D V D T L (11) V D = RT L P D (12) Plug in P D from above, V D = parenleftbigg RT L V γ A P A parenrightbigg 1 1 - γ (13) Since V C = V D , V C = parenleftbigg RT L V γ A P A parenrightbigg 1 1 - γ (14) 2
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To find P C , P C V C = nRT C (15) P C parenleftbigg RT L V γ A P A parenrightbigg 1 1 - γ = nRT A (16) P C parenleftbigg RT L V γ A P A parenrightbigg 1 1 - γ = P A V A (17) Solve this for P C , P C = P A V A parenleftbigg RT L V γ A P A parenrightbigg 1 γ - 1 (18) c) Find direction of heat flow for every interval A B : Since T B > T A
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