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Unformatted text preview: VERSION A 1. (20 points) PART I: SHORT ANSWER (a) (4 points) What is the first law of thermodynamics? Be sure to define all variables. Answer: The change in the internal energy of a system equals the heat Q it absorbs plus the work W done on the system. Δ E int = Q + W (1) Δ E int = E int (final)- E int (initial) = change in the internal energy of the system Q = heat absorbed by the system W = work done on the system. (Work done by the system would have the opposite sign.) Differential form: dE int = dQ + dW (b) (4 points) What is the constant volume molar specific heat C V of an ideal di- atomic gas in 2 dimensions? (Ignore vibrational degrees of freedom.) Explain your reasoning. Answer: C V = dQ dT fl fl fl fl fl V (2) From the first law of thermodynamics, for V = const and W = 0, Δ E int = Q (3) So we need to find Δ E int . To do this, we use the equipartition theorem which says that the internal energy per molecule is k B T/ 2 for each degree of freedom. Let’s add up the degrees of freedom. There are 2 translational degrees of freedom since we are in 2 dimensions and 1 rotational degree of freedom which corresponds to rotating in the plane about an axis perpendicular to the plane. Thus there are 3 degrees of freedom and the internal energy per molecule is 3 k B T/ 2. For 1 mole, the internal energy is E int = 3 2 RT (4) So the molar specific heat is C V = dE int dT = 3 2 R = 3 2 (8 . 314J / mol)) = 12 . 47J / mol where R is the gas constant. C V = 3 2 R = 12.47 J/mol 1 (c) (5 points) Sketch the electric field lines for 2 equal and opposite point charges.- + (d) (4 points) A hollow ball of aluminum floats in water. If the ball is heated (but does not melt), will the ball i. ride higher in the water ii. ride lower in the water iii. stay at the same height i. ride higher in the water Explain your answer....
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