ME235Lecture_10

# ME235Lecture_10 - 1 Thermodynamics Vm235 Thermodynamics...

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Unformatted text preview: 1 Thermodynamics Vm235 Thermodynamics Vm235 Lecture 10 Chapter 8 – Entropy We wish to define a ‘PROPERTY’ ( – not ‘path dependent’ like heat and work – ) that increases when disorder increases i.e. during irreversible spontaneous processes and not during reversible processes. What do we know? 1. Disorder is associated with heat ‘Q’ not work ‘W’ . 2. We don’t want either heat or work by themselves because they are path dependent . 3. We do know that a combination of heat and work can yield a property like in the 1 st Law: Δ U = δ Q – δ W. 4. We also know that temperature is a measure of the intensity of random motions and vibrations or disorder. At absolute T=0K all motions ceases. 5. We also showed, while define absolute temperature , that: Thus, there is a possibility of combining Q & T to define a property. L L H H T Q T Q = 2 L L H H T Q T Q = Let us examine the combination ‘Q/T’ that came out of the definition of absolute temperature. Recall that absolute temperature was defined by applying the 2nd Law to reversible engines. Now, adding ‘Q’ to a system increases disorder , however, we can add more ‘Q’ at higher temperatures than at lower temperatures because we can extract order or work out of it by running an engine between T H and T L . Lower the temp., more difficult to get work. Thus, the ratio ‘Q/T’ appears to be a measure disorder because ‘Q’ represents disorder & ‘T’ its conversion possibility. Thus: disorder ∝ Q , and disorder ∝ 1/T. : ; ' ' . Q Clausius inequality T where is for reversible processes δ ≤ = ∫ v disorder ∝ Q , and disorder ∝ 1/T. Next we proved that ‘Q/T’ is a PROPERTY by using the Clausius inequality: Entropy Generation for a control mass: ; T Q dS : & : process le irreversib an for Thus, process. reversible a in than larger is process le irreversib an in change Entropy . or S T Q same the for gen rev for dS is this irr for > + = ¡ ¢ £ ¡ ¢ £ 6 δ δ δ ; : ? ; : , : T or PdV dU TdS relations these have we state in change same the For work the is less much How PdV W W or W dU Q law first from Further Q Q S T TdS Q state in change same the for rev irr irr irr irr rev gen irr + = = < + = > ⇒ − = ¤ ¥ ¦ 6 6 δ δ δ δ δ δ δ δ N . : , gen out in Entropy write may we general In work lost S T W W PdV PdV dU S T W dU Q S T Q gen irr rev gen irr irr gen irr + − = Δ > + = ⇒ + = + + + §¤ §¥ ¦ §¤ §¥ ¦ δ δ δ δ δ δ δ δ 3 : . . ; : . . → = M C Q Q process le irreversib an for change Entropy system a or mass control M C T Q dS process reversible a for change Entropy δ δ δ ¡ ¢ £ '2' and '1' state between g integratin ; 2 1 2 1 1 2 . ....
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## This note was uploaded on 09/15/2010 for the course ME 235 taught by Professor Borgnakke during the Fall '07 term at University of Michigan.

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ME235Lecture_10 - 1 Thermodynamics Vm235 Thermodynamics...

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