# ps5 - Statistical Physics I(8.044 Spring 2009 Assignment 5...

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Unformatted text preview: Statistical Physics I (8.044) Spring 2009 Assignment 5 March 4, 2009 Due March 11, 2009 Please remember to put your name and section number at the top of what you turn in. Your FIRST TEST is Monday March 16 at the usual lecture time, 1-2 pm , in an unusual location: 3RD FLOOR OF WALKER MEMORIAL, AKA 50-340 . Readings By now you should have completed Chapters 1, 2 and 3.1-3.7 of Adkins and Chapter 1 of Baierlein. The reading for Chapter IV of 8.044 is Baierlein, Chapters 2 and 4.3 and the Notes on the Microcanonical Ensemble available on the web page. This reading is not needed for this problem set. Problem Set 5 1. Specific Heat Capacity of Water and Copper (4 points) The specific heat capacity of a substance is the heat capacity of a chunk of that substance per unit mass. If evaluated at constant pressure, it is denoted c P ; if evalu- ated at constant volume, it is denoted c V . (The lower case c is used for specific heat capacity, while the upper case C is used for the heat capacity of the entire chunk of substance, which is proportional to its mass.) In a calorimetric experiment used to measure the specific heat capacity of copper, 100 grams of copper is heated to 100 ◦ C by immersion in boiling water and is then quickly transferred into a vessel containing 200 grams of water at 15 ◦ C. The vessel has insulating walls of negligible heat capacity. After the copper and water have come to equilibrium, their temperature is measured to be 18.8 ◦ C. The specific heat capacity of water at room temperature is 4.18 (Joules/Kelvin)/gram. [Aside: 4.18 Joules is called a calorie.] Assuming that the specific heat capacities of both water and copper are constant over the range of temperatures concerned, what is the specific heat capacity of copper? Does this experiment measure c P or c V ? Would there be much difference between these quantities for copper under the conditions of this experiment? 1 2. Isothermal Compression and Heat Capacities of a Non-Ideal Gas (8 points) A certain gas has the equation of state P + a V 2 ( V- b ) = Nk B T and the internal energy U = cNk B T- a V where a , b , and c are constants. (a) Consider a quasistatic isothermal compression of this gas from an initial volume V 1 to a final volume V 2 < V 1 at temperature T . How much work has been done on the gas? (b) Calculate C V and C P for this gas....
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ps5 - Statistical Physics I(8.044 Spring 2009 Assignment 5...

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