161ASpring2010-Lecture12

161ASpring2010-Lecture12 - 1 Carnot Cycle We see that 1 1 =...

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Unformatted text preview: 1 Carnot Cycle We see that: 1 1-- = = γ γ a d b c c h V V V V T T a b d c V V V V = Which means that Now also from the isothermal parts of the carnot cycle: This is an important result. Temperature can be defined (on the absolute (Kelvin) scale) in terms of the heat flows in a Carnot Cycle. This is important since it works for any working fluid and does not depend on the properties of an Ideal Gas 2 Pressure Carnot Cycle Volume • • a b • d T h Q h Q c V nRT P h = γ V const P . = T c • c q=0 Q=0 V nRT P c = W 3 Adiabatic Reversible Process: q=0 Ideal gas Small adiabatic change (dV,dT) Grains of sand Adiabatic walls 4 The work for an adiabatic process adiabatic ( thermally isolated system) The amount of work needed to change the state of a thermally isolated system depends only on the initial and final states and not on the intermediate states. 2 1 = → q 2 1 → = W dU V P V 1 PV = Nk B T 1 PV = Nk B T 2 1 2 V 2 An adiabata is “steeper” than an isothermal: in an adiabatic process, the work flowing out of the gas comes at the expense of its thermal energy ⇒ its temperature will decrease. -- =- =- =-- → ∫ ∫ 1 1 1 2 1 1 1 1 2 1 1 1 1 1 ) , ( 2 1 2 1 γ γ γ γ γ γ V V V P dV V V P dV T V P W V V V V ⇒ 5/3 ≈ 1.67 (monatomic), 7/5 =1.4 (diatomic), 8/6 ≈ 1.33 (polyatomic) γ The pressure at everypoint on the adiabata obeys the following equation: 5 The p-V curve for an Adiabatic process V p adiabat : pV = constant isotherm : pV = constant γ = ( α +1)/ α ● In an adiabatic process, p , V , and T all change monatomic gas γ =(5/2)/(3/2) = 5/3 = 1.67 diatomic gas γ =(7/2)/(5/2) = 7/5 = 1.4 ● Adiabats (adiabatic p-V curves) are steeper than isotherms ● Adiabatic and isothermal processes are reversible-- 6 Homework Problem Imagine that we rapidly compress a sample of air whose initial pressure is 10 5 Pa and temperature is 22 C (= 295 K) to a volume that is a quarter of its original volume (e.g., pumping bike’s tire). What is its final temperature?volume (e....
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This note was uploaded on 09/08/2010 for the course CHEM 160 at San Jose State.

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161ASpring2010-Lecture12 - 1 Carnot Cycle We see that 1 1 =...

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