This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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) BDA3550 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...
View
Full Document
 Winter '09
 NateLewis
 Thermodynamics, isothermal processes

Click to edit the document details