l04 - 20.110J / 2.772J / 5.601J Thermodynamics of...

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20 .110/5.60 Fall 2005 Lecture #4 page 1 EXPANSIONS, THERMODYNAMIC CYCLES 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 Ideal gas d U = C v d From 1 st Law d = - d v d T = - d along path VV RT dT dV CdT pdV R TV = =− −= ⎛⎞⎛⎞ = − = ⎯⎯⎯⎯⎯⎯→ = ⎜⎟⎜⎟ ⎝⎠⎝⎠ ∫∫ 22 11 1 for i.g. 21 12 RC CC CR Define 1 CT γ ≡⇒ = For monatomic ideal gas: 3 5 2 ( 1 generally) 5 3 2 = => = [More generally the heat capacity for a molecular species has a temperature dependence that can be approximated as with a, b, and c tabulated.] =+ + 2 () a bT cT In an adiabatic expansion ( 2 > 1 ), the gas cools ( 2 > 1 ). And in an adiabatic compression ( 2 < 1 ), the gas heats up. 20.110J / 2.772J / 5.601J Thermodynamics of Biomolecular Systems Instructors: Linda G. Griffith, Kimberly Hamad-Schifferli, Moungi G. Bawendi, Robert W. Field
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20 .110/5.60 Fall 2005 Lecture #4 page 2 For an ideal gas (one mole) γ ⎛⎞⎛⎞ =⇒ = ⇒= ⎜⎟⎜⎟
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l04 - 20.110J / 2.772J / 5.601J Thermodynamics of...

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