THERMAL PHYSICS PHGN 341
Colorado School of Mines
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This 2 page Class Notes was uploaded by Donato Hoeger Jr. on Monday October 5, 2015. The Class Notes belongs to PHGN 341 at Colorado School of Mines taught by James McNeil in Fall. Since its upload, it has received 35 views. For similar materials see /class/219609/phgn-341-colorado-school-of-mines in Engineering Physics at Colorado School of Mines.
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Date Created: 10/05/15
Physics 341 Fundamental Equations Energy First Law AU Q W Ideal Gas Law PV nRT NkT Equipartitian U N f kT Kinetic Theory vrms M Processes Isothermal compression W NkT ln ViVf Adiabatic compression PV39Y constant 7 l 39 7 7 3U 7 7 3H Heat Capacity CV 7 ltV 7 x Op 7 ltP 7 WM Latent Heat L Heat needed for phase transition per unit mass Enthalpy H U PV Magnetic dipole U 7 E Entropy De nition 5 16an Second Law In any process the entropy increases or stays the same AS 2 0 Approximate model multiplicities Approximations Nl V ZWNNNe N ln 1 z 2 z 7 272 N 7 N 7 7 Twostate system 927stateNNT 2 WII LNT NT17 N NT Einstein solid QESN q byfill l 2 Wlt1 q1 N v 7 22 N N ldeal Gas deealN V U 2 eg Where v0 Approximate model entropies Twostate system 527mmN NT 2 7kN 1n 17 1n 1 7 Einstein solid SE5N q 2 k qln l Nq Nln l qN ldeal gas SackurTetrode deealN V U 2 kN 1n Where v0 Sth 47rmU Engines and Refrigerators Engine efficiency e Ne work S l 7 T Heat in W Refrigerator coefficient of performance cop H47H1 H 7H1 3 Throttling process refrigerator cop Heat out Ta Work in 7 Th7T4 Steam engine efficiency e 2 l 7 Paramagnetic magnetization M NM tanh Thermodynamic Properties Thermodynamic potentials US V N HS P N FT V N CT P N Thermodynamic relations dUTdS7PdVidN dHTdSVdPndN dF 7SdT 7 PdV ndN dG 7SdT VdP ndN Partial derivative relations gtVN T M P N gtRN T M V SP M at 75 a 7 7P at i an 7s an 7 v an i Maxwell Relations dUz aw 7 any de an an dF VN TN dG PN 7TN 3P 5251 L Claussius Clapeyron Relation WG V2411 W Boltzmann Factor and the Partition Function Boltzmann Factor and Probability Ps Partition Function Z ES e ES kT 1 Average Values a ES Q5Ps i 773 32 2 Velocity distribution Dv 47rv2 e mv 2 2state paramagnet Z2mne 2 cosh nBo Harmonic Oscillator ZHO l 7 e h 1 Diatomic Molecule rotations ZN Where f5 l distiguishable and f5 indistinguishable ldeal gas ln Zideal N ln 32th 1 Relation to Helmholtz Free Energy F 716T an Chemical potential Milieu TV 716T ln 32th Gibbs Factor and Quantum Statistics Gibbs factor PsN5 w Where E5 is the single particle energy Grand Partition Function Z ESNS e NdEs H Density of States dn 2Vg7ldkt9kp 7 k N DOS in terms of energy nonrelatiVistic dn 90612de7 Where 90 Wk 2m FermiDirac Statistics FD s m EF nonrelatiVistic 22 kT E 2 2 Average energy nonrelatiVistic UFD go fem deeTxfi Mm S F ENE NT2 BoseEinstein Statistics 53 s E 0 for photons and phonons e3lt 5 gt71 M Blackbody Radiation th 87571 2 I 0T4 AMT 2989 gtlt10 3 mK Debye Theory of Solids TD 13 gs 67313 4 T T 3 TltltT 4 Uphomm will f0 13 efildz D SngkTAl Additional Information Constants R 8315 JmolK Is 1381 X 10 23 JK 8617 gtlt10 5 eVK NA 6022 X1023 h 27rh 6626 gtlt10 34 Js 1 atm 1013X105 Pa TSTP 298 K 1 eV l6gtlt10 1g J a 567 X 10 8 VVm2 K4 he 1240 eV nm he 1973 eV nm u 166 gtlt10 27 kg Integrals fem dz z 6 nl fem dz 6 12 3 fem dz z2 6 12 70 3 0 2n1 712100 nisi 0 3 f0 dII e 2f0 dsse 2af0 o 4 00 z 77 a 71L ezildz 15a f0 ez1dI a 1
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