JTueSep16

# JTueSep16 - 1 Thermodynamics 19,340 ft According to...

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Unformatted text preview: 1 Thermodynamics 19,340 ft According to Wikipedia it is the highest point on earth with mobile phone coverage! Two hundred miles south of the equator 2 Adiabatic Expansion In an adiabatic expansion no heat is transferred into or out of the system. q = 0 and ∆ U = w This equation says that the energy to do any work can only come the internal energy of the system. This is important because it means that if work is done the temperature must drop. Integrating the expression for C V yields ∫- = = ∆ PdV w U V V T U C ∂ ∂ = ∫ ∫- = = ∆ PdV dT C U V McQ & S page 774 3 Reversible Adiabatic Expansion Replace P with nRT/V Divide by T and remove the constants from the integral Integrate dV V nRT dT C V V T T V ∫ ∫ - = 2 1 2 1 - = 1 2 1 2 ln ln V V nR T T C V dV V nR dT T C V V T T V ∫ ∫ - = 2 1 2 1 dV V nR dT T C V V T T V ∫ ∫ - = 2 1 2 1 1 1 4 But C P – C V = R for one mole of gas The ratio C P /C V is given the symbol γ (Greek lower case gamma) then - = 1 2 1 2 ln ln V V nR T T C V ( 29 -- = 1 2 1 2 ln ln V V C C T T C V P V ( 29 -- = 1 2 1 2 ln ln V V C C C T T V V P ( 29 -- = 1 2 1 2 ln 1 ln V V T T γ 5 Take antilogs of both sides Replace T with PV ( 29 -- =...
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JTueSep16 - 1 Thermodynamics 19,340 ft According to...

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