06availability

# 06availability - Availability From chapter 8 VW&S control...

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Availability From chapter 8 VW&S control volume in uniform state, uniform flow process USUF, irreversible Q c.v . and W c.v. what if process were reversible, how much work would have been done if the process had been reversible <= reversible heat engine + W rev = W c_v_rev W c reversible heat transfer takes place through reversible heat engine (8.1) with output W c I = irreversibility = W rev W cv first law for uniform state, uniform process . .. from first_law.mcd uniform state, uniform flow process (USUF) (5.54) = (8.3) m i gz i n n 2 n h e 2 gz e ... V i V e Q c_v_rev + h i + + + + 2 = 2 n m e m 2 2 2 V 2 V 1 W c_v_rev + + + + + + gz 2 gz 1 9/27/2006 1 u 2 m 1 u 1 2 2

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for the reversible heat engine . .. W c Q o Q c_v_rev = from second law Δ S for Q o and Q c_v_rev are the same, Q o at constant temperature t d and Q o T o 0 Q_dot c_v_rev d that is express as integral of rate Δ S = Δ S c_v_rev Q o T o Δ S Δ S c_v_rev t = = T uniform state => T constant in c.v. t 0 t t Q_dot c_v_rev 0 Q o Q_dot c_v_rev T Q_dot c_v_rev d t t = = T T o 0 substituting into . .. (8.4) W c Q o Q c_v_rev T o dt Q c_v_rev = = T t Q_dot c_v 0 + from second law m 2 s 2 m 1 s 1 m e s e m i s i n n substituting (8.5) into (8.4) . .. W c Q o Q c_v_rev = m 2 s 2 T o = ( ) ( ) = + (7.56) = when also for USUF dt T reversible (8.5) ( ) ( ) m 1 s 1 m e s e so . .. the bottom line, substitute (8.3) rearranged and (8.6) into (8.1) W rev W c_v_rev m e gz e Q c_v_rev m i s i W c n n + = m i 2 2 2 V i V e W rev Q c_v_rev + h i h e + + + + = gz i u 1 ... 2
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06availability - Availability From chapter 8 VW&S control...

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