Thermodynamics and Statistical Physics

Abstract

DISCLAIMER: This is a sample PhD qualifier exam to only demonstrate the typical level of question that may be posed by the GRASP. Students must not infer anything regarding the content of their exam based on these examples; questions may be drawn from the full range of the topic. Choose four out of the following five problems. All problems are weighted equally. Show and explain all your work for full credit. 1. An ice cube (mass 30 g) at 0 • C is left sitting on the kitchen table, where it gradually melts. The temperature in the kitchen is 25 • C. The specific heat of water is 4.187 kJ kg −1 K −1. The latent heat of fusion of water is 334 kJ kg −1. (a) Calculate the change in the entropy of the ice cube as it melts into water at 0 • C. (Don't worry about the fact that the volume changes somewhat.) (b) Calculate the change in entropy of the water (from the melted ice) as its temperature rises from 0 • C to 25 • C. (c) Calculate the change in the entropy of the kitchen as it gives up heat to the melting ice/water. (d) Calculate the net change in the entropy of the universe during this process. Is the net change positive, negative, or zero? Is this what you would expect? 2. Use the thermodynamic identity to derive the heat capacity formula C V = T ∂S ∂T V , which is occasionally more convenient than the more familiar expression in terms of U. Then derive a similar formula for C P , by first writing dH in terms of dS and dP , where the enthalpy H = U + P V. 3. A power plant produces 1 GW (10 9 watts) of electricity at an efficiency of 40%.