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Unformatted text preview: 5.60 Spring 2004 Lecture #6 page 1 Reversible Adiabatic Expansion (or compression) of an Ideal Gas one mole ideal gas reversible adiabatic 1 mol gas (V1,T1) = 1 mol gas (V2,T2) Adiabatic fi dq = 0 Ideal gas fi Reversible fi dU = CvdT dw = -pdV \ From 1st Law dU = -pdV fi CvdT = -pdV along path
dT dV = -R T V CV dT = - pdV p= fi CV RT
V CV T2 T1 V2 dV dT T V = - R fi CV ln 2 = - Rln 2 V1 V T T1 V1 Integrating: T2 ^ T ~ 1 CV V ^ = 1~ V2 R T ^ V ^ fi 2~ = 1 ~ T1 V2 Cp -1 R CV T ^ V ^ CV C p -C V =R for i.g. 2 ~ = 1 ~ T1 V2 Define Cp g CV fi T2 ^ V1 ^ T ~ = V ~ 1 2 g -1 For monatomic ideal gas: 3 R 2 g = 5 (> 1 generally) 5 3 C p = R 2 CV = Since g > 1 fi g - 1> 0 5.60 Spring 2004 Lecture #6 page 2 In an adiabatic expansion (V2 > V1), the gas cools (T2 < T1). And in an adiabatic compression (V2 < V1), the gas...
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This note was uploaded on 04/23/2009 for the course GENERAL CH 1230 taught by Professor Unknown during the Spring '04 term at Toledo.
- Spring '04