Lecture 25 PES Su 2011 annotated0

# Lecture 25 PES Su 2011 annotated0 - Thermodynamics I...

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Unformatted text preview: Thermodynamics I Lecture 25: Clausius’ inequality, Entropy, increase in entropy principle Paul E. Sojka Summer 2011 This Lecture • Clausius’ inequality usage • Entropy • The increase in entropy principle Entropy Entropy is a property, BUT A NON- CONSERVED ONE It’s a natural result of the 2 nd Law Clausius’ Inequality Clausius’ inequality will be used to develop entropy ,, irrevC rev HH b HCHC QQ QQ Q TT TT T δ =-<=- ∫ & Clausius’ Inequality (contd.) Consider the following: There are two cycles between states 1 and 2 c Cycle 1: A and C (both internally reversible) c Cycle 2: B and C (both internally reversible) Does the Clausius integral depend on the path? No! It’s zero in both cases. SO IT’S A PROPERTY! Entropy c We define the property entropy based on a reversible heat transfer process: c For a closed system c For a thermal reservoir nt.rev. Q dS T δ = 2 21 1 nt.rev. Q SSS T δ ∆=-= ∫ , HC RHC HC QQ SorT T TT ∆=-+ c o n s t a n Entropy Generation 2 1 1 R Q S T δ - ∫ 21 12 brevirrev QQQ TT T δ δ δ +≤ ∫∫∫ & Consider two paths, one irreversible and one internally reversible, connecting states 1 and 2. • Write Clausius’ inequality for the cyclic process R I 1 2 12 21 21 rrevirrev QQ SS TT δ δ ⇒-≤-= + ∫∫ Entropy Generation (contd.)Entropy Generation (contd....
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Lecture 25 PES Su 2011 annotated0 - Thermodynamics I...

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