ps1rev - Statistical Physics I(8.044 Spring 2009 Assignment...

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Unformatted text preview: Statistical Physics I (8.044) Spring 2009 Assignment 1 February 4, 2009 Due February 11, 2009 Please remember to put your name and section number at the top of what you turn in. Announcements • The 8.044 web site is http://web.mit.edu/8.044/www . If you wish to switch recitation sections, you must request the change on the web site. • Sections begin Thursday February 5. Readings • The first 8.044 reading assignment is pages 1-86 of P.W. Atkins book The 2nd Law: Energy, Chaos and Form . Chapter 1 of 8.044 will follow this text, meaning that it should be very helpful for you to be ahead of the lectures in your reading of it. We have scanned the first five chapters of this book and made them available on the course web page. • The second 8.044 reading assignment is Notes on Probability for 8.044 by Prof. Grey- tak. It is also available on the course web page. This reading is not needed for this week’s problem set, but I have asked your recitation instructors to begin teaching you some concepts in probability, via the use of examples, before we get to it in lecture. Problem Set 1 1. How Large is “Thermodynamically Large”? (12 points) Thermodynamics is about new phenomena and concepts that arise in the physics of objects made of “large” numbers of particles. In this problem, we get a sense of how large is large, for a few human-scale objects, and then attempt to visualize the meaning of the scale of the numbers that arise. (a) The ideal gas equation of state, familiar from chemistry, can be written PV = Nk B T . Here, P and V are the pressure and volume, N is the number of gas molecules in the volume V , k B = 1 . 381 × 10- 16 ergs K- 1 is Boltzmann’s constant, and T is the temperature in degrees Kelvin, K. 1 [Water freezes at 273 K and boils at 373 K; 0 K is absolute zero, the meaning of which we shall get to later in 8.044.] Assuming that air is well-approximated as an ideal gas, how many molecules are there in one cubic meter of air at a pressure of 1 atmosphere at room tempera- ture? [1 atmosphere is 1 . 013 × 10 6 dyn/cm 2 . Lets take room temperature to be 293 K.] (b) How many water molecules are there in a cup of water? [There are Avogadro’s number N A = 6 × 10 23 carbon atoms in 12 g of carbon. You can take the masses of hydrogen, carbon and oxygen atoms to be in the ratio 1:12:16. And, lets say that a cup is 1/4 of a litre.] (c) Your answers to both parts (a) and (b) should be in the vicinity of 10 24 − 10 25 ....
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ps1rev - Statistical Physics I(8.044 Spring 2009 Assignment...

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