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Unformatted text preview: Print your name clearly: Signature: “I agree to neither give nor receive aid during this exam.” Final Exam for Physics 176 Professor Greenside Wednesday, April 29, 2009 This exam is closed book and will last the entire exam period. Please note the following: 1. Please hand in your 1page of notes with your exam. 2. Before answering any questions, take a moment to look over the entire exam and get a sense of its length, what kinds of questions are being asked, and which questions are worth the most points. 3. Truefalse and multiple choice questions should be answered on the exam itself. 4. All other questions should be answered on the extra blank pages. If you need extra pages during the exam, let me know. 5. Please write your name and the problem number at the top of each extra page. 6. Please write clearly. If I can not easily understand your answer, you will lose credit. 7. Unless otherwise stated, you must justify any written answer with enough details for me to understand what you are doing. 8. Please feel free to ask me questions during the exam if the wording of a problem is not clear. The following data and formulas may be useful: k ≈ 1 . 4 × 10 23 J K , h ≈ 6 . 7 × 10 34 J · s , g ≈ 10 m s 2 , N A ≈ 6 . × 10 23 molecules mole . (1) P V = NkT, Δ U = Q + W, U = N f ( kT/ 2) , dU = T dS P dV + μ dN. Ω( n, q ) = n + q 1 q ¶ , x ! = Γ( x + 1) ≈ √ 2 πx ‡ x e · x for x 1 . (2) S = k ln Ω , S = Q T , Δ S = Z T 2 T 1 C ( T ) T dT. (3) F = U T S, dF = S dT P dV + μ dN, Z = X s e βU ( s ) , F = kT ln( Z ) . (4) G = U T S + P V, dG = S dT + V dP + μ dN, G = Nμ. (5) Φ = U T S μ N, d Φ = S dT P dV N dμ, Z = X s e β [ U ( s ) μN ( s )] , Φ = kT ln( Z ) . (6) 1 Z = 1 N ! Z N 1 , Z 1 = V V Q Z int , V Q = h √ 2 πmkT ¶ 3 , μ gas = k T ln V Z int NV Q ¶ . (7) p n = h λ n = hn 2 L , electron = p 2 2 m = h 2 8 mL 2 ( n 2 x + n 2 y + n 2 z ) . (8) F = h 2 8 m 3 N πV ¶ 2 / 3 , U = 3 5 N F , P = 2 3 U V , T D = hc s 2 k 6 N πV ¶ 1 / 3 . (9) I = L 4 πd 2 , L = ( 4 πR 2 ) × σ T 4 . (10) dP dT ¶ 12 = S 1 S 2 V 1 V 2 = L 12 T ( V 1 V 2 ) , Δ P = ρ g Δ z. (11) 1 1 + x ≈ 1 x + x 2 x 3 + . . . , 1 + x + x 2 + . . . + x N 1 = 1 x N 1 x . (12) Problems That Require Writing Please write your answers to the following problems on extra blank sheets of paper, and make sure to write your name and the problem number at the top of each sheet. Unless otherwise stated, you need to justify your answers to get full credit . 1. (6 points) List six distinct criteria that a system has to satisfy to be in thermodynamic equilibrium. (No justification needed here.) 2. (8 points) Draw a representative phase diagram (with horizontal axis the temperature T and vertical axis the pressure P ) that includes all the features that are typically observed in the phase diagram of a pure substance like carbon dioxide. Make sure to label clearly all features and regions of your plot....
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 Spring '08
 Behringer
 Physics, Thermodynamics, surface temperature, T2 T2 T1

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