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5_60_lecture5

# 5_60_lecture5 - MIT OpenCourseWare http/ocw.mit.edu 5.60...

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MIT OpenCourseWare http://ocw.mit.edu 5.60 Thermodynamics & Kinetics Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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5.60 Spring 2008 Lecture #5 page 1 Reversible Adiabatic Expansion (or compression) of an Ideal Gas 1 mole gas ( V 1 , T 1 ) = 1 mole gas ( 2 , 2 ) adiabatic đ q = 0 Reversible đ w = - p d V Ideal gas d U = C v d T From 1 st Law d = - d v d = - d along path =− pdV dT dV CdT C R RT = ⎛⎞⎛⎞ RC p 1 2 2 dV 2 1 = R for i.g. 2 1 = − = ⎯⎯⎯⎯⎯⎯→ = ⎜⎟⎜⎟ 1 1 1 1 ⎝⎠⎝⎠ 2 2 2 1 γ 1 Define = 1 2 = 3 For monatomic ideal gas: 2 = 5 ( > 1 generally) = 5 3 2 In an adiabatic expansion ( 2 > 1 ), the gas cools ( 2 > 1 ). And in an adiabatic compression ( 2 < 1 ), the gas heats up. ⎛⎞ For an ideal gas (one mole) = pV 2 = 1 11 = ⎜⎟ 2 2 ⎝⎠ 2 1 is constant along a reversible adiabat For an isothermal process = constant pV = constant
5.60 Spring 2008 Lecture #5 page 2 p V 2

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5_60_lecture5 - MIT OpenCourseWare http/ocw.mit.edu 5.60...

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