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Fa08-MT1-Charman-Soln

# Fa08-MT1-Charman-Soln - University of California Berkeley...

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Unformatted text preview: University of California, Berkeley Physics 7B Lecture 002: Midterm #1 Solutions Instructor: A. E. Charman Fall 2008 1. Thrifty Thermo and Quick Kinetics (SHORT ANSWERS) [50 points] (a) [4 points: 1/2 point for each correct answer] Note that we made no assertion that the process was quasistatic or reversible.... i. Δ T = 0 D (Isothermal) ii. Δ V = 0 C (Isochoric) iii. Q in = 0 A (Adiabatic) iv. Δ P = 0 B (Isobaric) v. Δ S = 0 E (Isentropic) vi. Δ E = 0 for an ideal diatomic gas D (Isothermal) (since Δ E ∝ Nk Δ T ) vii. W by = 0 for a monatomic van der Waals gas C (Isochoric) (since compressional W ∝ Δ V ) iix. sudden free expansion of a van der Waals gas in an insulated container A (Adiabatic) (Δ S > 0 in a free expansion; Δ T < 0 because of inter-particle forces in non-ideal gas) (b) [6 points: 1/2 point for each correct answer] Recall from lecture that a physical observable is INTENSIVE if it represents the degree or intensity of something, that is, does NOT scale proportionally with the size of the system, and is EXTENSIVE if it represents the amount or quantity of something, and does scale proportionally with the size of the system. To determine whether a quantity is intensive or extensive (or neither), just imagine combining two equivalent copies of the ”system” together into a bigger system: if the quantity of interest doubles, it is extensive, if it remains the same, it is intensive. i. volume EXTENSIVE ii. temperature INTENSIVE iii. number of molecules EXTENSIVE iv. (absolute) pressure INTENSIVE v. gauge pressure INTENSIVE (the difference between intensive quanitties is intensive) vi. entropy EXTENSIVE vii. specific heat at constant pressure INTENSIVE iix. total heat capacity at fixed volume EXTENSIVE ix. number density (i.e., chemical concentration) INTENSIVE x. total mass EXTENSIVE xi. mass density INTENSIVE xii. work done during an isothermal expansion doubling volume EXTENSIVE (c) [10 points: 1 point for each correct answer] ( α ) In Figure (i), the net work performed BY the system is W = I PdV =- area of ellipse =- π 3 P- 2 P 2 5 V- V 2 =- π P 2 4 V 2 =- πP V , so the magnitude of the work is | W | = πP V . ( β ) In the P- V plane, the cycle is counter-clockwise (compression happens at a higher pressure than the expansion), so the net work is done ON THE SYSTEM by the environment. 1 ( γ ) In Figure (ii), the net heat flow into the system is given by Q = I TdS = area of triangle = 1 2 (5 S- S )(3 T- T ) = 1 2 4 S 2 T = 4 S T , so the magnitude of the work is | Q | = 4 S T . ( δ ) In the T- S plane, the cycle is clockwise, meaning more heat flows in than out. Thus the net heat flow is INTO the system, from the surroundings....
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Fa08-MT1-Charman-Soln - University of California Berkeley...

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