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Sp04-MT1-Smoot-Exam - Department of Physics University of...

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Department of Physics University of California, Berkeley Mid-term Examination 1 Physics 7B, Section 2 6:00 pm - 8:00 pm, 24 February 2004 Name: SID No: Discussion Section: Name of TA: 1
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Score: Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 2
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Answer all six problems. Write clearly and explain your work. Partial credit will be given for incomplete solutions provided your logic is reasonable and clear. Cross out any parts that you don’t want to be graded. Enclose your answers with boxes. Express all numerical answers in SI units . Answers with no explanation or disconnected comments will not be credited. If you obtain an answer that is questionable, explain why you think it is wrong. Constants and Conversion factors Avogadro number, N A 6 . 022 × 10 23 Universal gas constant, R 8.315 J · mol - 1 · K - 1 = 1.99 cal · mol - 1 · K - 1 Boltzmann constant, k 1 . 381 × 10 - 23 J · K - 1 Stefan-Boltzmann constant, σ 5 . 67 × 10 - 8 W · m - 2 · K - 4 Acceleration due to gravity, g 9.8 m · s - 2 Specific heat of water 1 kcal · kg - 1 · C - 1 Heat of fusion of water 80 kcal · kg - 1 1 atm 1 . 013 × 10 5 N · m - 2 1 kcal 4 . 18 × 10 3 J 1 hp 746 W 1 liter 10 3 cm 3 Some useful equations Δ L = αL Δ T W = pdV Q = mc Δ T Q = nC Δ T, where C = C V or C P v = 8 kT πm dN v dv = 4 πN m 2 πkT 3 2 v 2 e - mv 2 2 kT PV γ = constant TV γ - 1 = constant γ = C P C V dQ dt = σ AT 4 dQ dt = - κA dT dx 3
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1. [25 points] Short Questions (a) [5 points] Circle T or F for True or False T F (i) The heat capacity of a body is the amount of heat that it can store at a given temperature. T F (ii) If the absolute temperature of a body triples, the rate at which it radiates energy increases by a factor of 9. T F (iii) When a system goes from equilibrium state 1 to state 2, the change in the internal energy is the same for all processes. T F (iv) The internal energy of a given amount of an ideal gas at equilibrium depends only on its absolute temperature. T F (v) For any material that expands when heated, C P is greater than C V . T F (vi) Pressure and Temperature are state variables. T F (vii) For a solid the mean distance between atoms is 2 × 10 - 10 m. T F (viii) The Carnot efficiency changes by the same amount from either increasing the hotter temperature reservoir by 10% or decreasing the lower reservoir temperature by 10% to within 1%. T F (ix) A good emitter of radiation is a good absorber of radiation. T F (x) According to the principle of equipartition, energy is shared equally among the active degrees of freedom in an amount of 1 2 kT on average. 4
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(b) [5 points] Circle correct answer (i) A scuba diver releases a spherical air bubble 3-cm diameter at a depth of 14-m in water at 298 K. Approximately what is the air bubble’s radius just as it reaches the surface, if the temperature stays constant. Take the density of water to be 1000 kg/m 3 .
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