5_First_law_part_3

5_First_law_part_3 - pV + V p = nRT (1) Difference form of...

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Δ U = n Δ TC m , V Δ U = p Δ V n Δ T = p Δ V C m , V n Δ T = p Δ V + V Δ p C m , p C m , V = p C m , V Δ V p Δ V + V Δ p = nR Δ T (1) Difference form of ideal gas law Equating (2) and (3) and rearranging (2) Adiabatic conditions Substituting for R in (1) and equating Δ p p + C m , p C m , V Δ V V = 0 dp p + C m . p C m , V dV V = 0 Integrating and allowing γ =Cp/Cv pV γ = constant p 1 V 1 = p 2 V 2 T 1 V 1 1 = T 2 V 2 1 Reversible Adiabatic Expansion (3) DeFnition of U R = C m , p C m , V p 2 T 1 / 1 = p 1 T 2 / 1
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What is γ for a monatomic gas? 3 translational degrees of freedom γ =(3+2)/3=5/3=1.7 Diatomic? 3 translational, two rotational γ =(5+2)/5=7/5=1.4 γ = f + 2 ( ) / f where f is the number of degrees of freedom in the molecular motion: translation, rotational, vibrational How do we calculate γ ?
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The work done in reversible adiabatic process: w = C V Δ T = p 1 V 1 p 2 V 2 ( ) / γ− 1 ( ) Isothermal
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This note was uploaded on 11/28/2011 for the course CHEM 300 taught by Professor N.gerber during the Fall '11 term at S.F. State.

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5_First_law_part_3 - pV + V p = nRT (1) Difference form of...

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