11 - First Law

# 11 - First Law - 45 46 Heat Capacities Why is c v = 3/2R A...

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Unformatted text preview: 45 46 Heat Capacities Why is c v = 3/2R? A C D B 1 2 10 20 30 Volume (liters) Pressure (atm) Constant volume change: work = -P ext ' V = 0 ' U = q+w, then ' U = q and q v = nc v ' T = 3/2nR ' T U = 3/2k B T per particle; =3/2nRT for a molar amount of particles Also ' U = q + w = heat + work and q = nc v,p ' T c v = 3/2R 47 Heat Capacities c p A C D B 1 2 10 20 30 Volume (liters) Pressure (atm) Constant P change: work ¡ ' U = 3/2nR ' T = q + w = heat + work and q = nc v,p ' T For a constant pressure expansion/compression of an ideal gas, use c p So c p = 5/2R q+w = ' U (= 3/2 nR ' T) = nc p ' T ¡ P ext ' V 3/2nR ' T = nc p ' T - nR ' T since PV = nRT then -P ext ' V = -nR ' T 3/2R = c p- R dividing both sides by n ' T 48 First Law of Thermodynamics Midterm will cover through next Tuesday¡s Lecture Review Session for MidTerm will be announced Monday in class 49 Other Pathways J atm l w q U Green 1520 15 ¡ ¢ ' How about the green path? Why? Because ' U is a state function ¡ it is pathway independent = all pathways A Æ B 50 Enthalpy V P q V P q w q U P ext P P ' ¡ ' ¡ ¢ ' The work that we have done implies that there is another state function involved here aside from ' U , the internal energy at constant Pressure (i.e. P = P ext ) 51 Enthalpy V P q V P q w q U P ext P P ' ¡ ' ¡ ¢ ' H PV U V P U q P P ' ¢ ' ' ¢ ' ) ( PV U H ¢ Thus, rearranging: Subscript implies constant P Note that q p is in terms of U, P, and V ¡ all are state functions, and so q p is a state function The state function is enthalpy, or H 52 Enthalpy ¡ ¢ PV T nc V ' £ ' ¡ ¢ PV U H ' £ ' ' 53 ¡ ¢ PV U H ' £ ' ' Enthalpy (defined more generally) ¡ ¢ PV T nc V ' £ ' ) ( R c T n T nR T nc V V £ ' ' £ ' T nc P ' T nc H P ' ' 54 ¡ ¢ PV U H ' £ ' ' Enthalpy T nc H P ' ' Why does ' H have to be a state function? Because U, P, and V are all state functions . Enthalpy is very important ¡ we will refer back to it several times 55 A C D B 1 2 10 20 30 Volume (liters) Pressure (atm) BDA-3550 J 2030J -1520 J 1 2 10 20 30 P V Work ACB 1 2 10 20 30 P V Work BDA Net 2020 J -2020J Efficiency = work net /q in = 2020J/5570J = 36% Efficiency of this Cycle Net work ACBDA 56 Extracting Work from a System P Volume Figure LS3.1. Two different pathways between A and B. The work for each pathway is represented by the shaded area. Note that if we...
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11 - First Law - 45 46 Heat Capacities Why is c v = 3/2R A...

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