Lecture 15

Lecture 15 - Review Chap 19:5-8Adiabatic Processes...

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May 27, 2008 Physics 40B Lecture 15 1 Chap. 19:5-8Adiabatic Processes Review Monatomic ideal gas: U = 3/2 nRT, (internal energy only depends on T ) C V = 3/2 R , C P = 5/2 R, γ = C P /C V = 1.67 For diatomic gases , U = 5/2nRT, C V = 5/2 R, C P = 7/2 R, γ = 7/5 = 1.4 ThermodynamicWork : dW = pdV W = pdV V i V f " Isothermal Process with Ideal Gas: W = pdV V i V f " = nRT V # \$ % & ( dV V i V f " = nRT dV V # \$ % & ( V i V f " W = nRT ln V f ) ln V i ( ) = nRT ln V f V i # \$ % & ( W = nRT ln p i p f # \$ % % & ( ( First Law: Δ U = U f - U i = Q - W dU = dQ - dW Isochoric (isovolumetric) : constant volume, dV = 0, W = 0, Δ U = Q = nC V Δ T Isobaric : constant pressure, dp = 0 W = p(V f - V i ) = p Δ V, Q = nC p Δ T Isothermal : constant temperature, dT = 0 For ideal gas: Δ U = 0, W = Q Adiabatic : dQ = 0 , no heat added, Δ U = - W Cyclic (i = f): Δ U = 0, W = Q

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May 27, 2008 Physics 40B Lecture 15 2 Adiabatic Expansion of Ideal Gas Remove mass from piston allows gas to expand Previously, for an isothermal expansion, Δ U = 0, Q = W pV = constant, T f = T i W = nRT ln(V f /V i ) Consider adiabatic expansion with Q = 0, Δ U = - W, T decreases
May 27, 2008 Physics 40B Lecture 15 3

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