Thermal Expression - Physics for Scientist and Engineers - Past Paper, Exams of Engineering Physics

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University of California, Berkeley Physics 7B, Lecture 001, Spring 2012 (Xiaosheng Huang) Midterm 1 Tuesday, 2/21/2012 8:00 - 10:00 PM Total Points: 100 Note: You are allowed one handwritten formula card (3%" by 5”, double sided). No calculators or any other electronic devices are permitted. Show all work, and take particular care to explain what you are doing. Please use the symbols described in the problems, define any new symbols that you introduce, and label any drawings that you make, 1. Thermal Expansion [20 pts] Consider a house in Berkeley made out of ordinary construction materials with a square base a on each side and height h. The fraction of air that is Nz (molecular mass = Mo) is f. In this problem you may find the following useful: 1/(+x) = | =x for small x. (Please be sure to justify using it — that is, provide reasoning that x is indeed small.) a) Estimate how many air molecules fill the interior space of the house at night when the air inside is at temperature T and pressure P, What assumptions have you made for the estimate? b) The walls of the house have a linear expansion coefficient a. If during the course ofa typical day the temperature of the walls changes by AT > 0, what is the fractional change in the interior volume? c) Assume that the pressure outside is the same during the day. If the house is NOT air tight, what is the fractional change in the number density of molecules (i.e., number per unit volume) corresponding to this temperature rise? Fig.1