Download Test 1 Problems - Thermodynamics and Statistical Mechanics | PHYS 4420 and more Exams Physics in PDF only on Docsity! Test I (20 points per problem) Thermo. & Stat. Mech., PHYS 4420, Spring 2009 1. Consider the following system: oubvT a vTu RTdvbP 2 2 ),( , where are positive constants. oudba ,,, (a) Obtain . vc (b) Obtain . Pc (c) Obtain the equation for the curve for the quasi-static (reversible) adiabatic process. vT This gas undergoes the (Gay-Lussac—Joule) free expansion to volume . The initial temperature of the gas is and the initial (specific) volume is . 12 2vv 1T 1v (d) Calculate , the final temperature of the gas. 2T (e) Determine the (specific) entropy change of the gas during this process. Your answers must be expressed in terms of the initial values and (and of course the constants appearing in the above expressions). 1T 1v 2. The Helmholtz free energy of a system is given by VT a VTF 4 3 ),( . Consider the Carnot cycle (consisting of two isotherms, at 21 TT , and two reversible adiabats) for this system. Explicitly calculate the efficiency of the Carnot cycle for this specific system. That is, you must start from the definition, received total Q W , and work out and from “scratch”. You must express you final answer in terms of and . totalW receivedQ 1T 2T (Simply quoting the obvious result, citing the 2nd law, will yield zero credit. You have to use the equation of state, internal energy, etc. [obtained from ], and explicitly calculate the necessary quantities for the relevant segments of the cycle.) ),( VTF 3. The chemical potential of a single-component gas is given by )( ln),( 2/5 bP T aRTPT , where are positive constants. ba, (a) Obtain the equation of state of the system. (b) Obtain the constant-pressure specific heat of the system . Pc (c) Consider that the above gas undergoes the Joule-Thomson “throttling process” from to ( ). Discuss whether the gas is cooling or warming during this process. You need to make some quantitative assessment supporting your answer (i.e., it is not a “yes or no” question). 1P 2P 21 PP
