= T. (kj/k) (kj/k) 0 (kj/k) int rev. Chapter 6 SUMMARY

Size: px

Start display at page:

Download "= T. (kj/k) (kj/k) 0 (kj/k) int rev. Chapter 6 SUMMARY"

Tyler Fletcher
5 years ago
Views:

1 Capter 6 SUMMARY e second la of termodynamics leads to te definition of a ne property called entropy ic is a quantitative measure of microscopic disorder for a system. e definition of entropy is based on te Clausius inequality given by δ Q 0 (J/K) ere te equality olds for internally or totally reversible processes and te inequality for irreversible processes. Any quantity ose cyclic integral is zero is a property and entropy is defined as ds δ Q = int rev (J/K) For te special case of an internally reversible isotermal process it gives S = Q o (J/K) e inequality part of te Clausius inequality combined it te definition of entropy yields an inequality non as te increase of entropy principle expressed as Sgen 0 (J/K) ere S gen is te entropy generated during te process. Entropy cange is caused by eat transfer mass flo and irreversibilities. Heat transfer to a system increases te entropy and eat transfer from a system decreases it. e effect of irreversibilities is alays to increase te entropy.

2 Entropy is a property and it can be expressed in terms of more familiar properties troug te ds relations expressed as and ds = du +dv ds = d - vd ese to relations ave many uses in termodynamics and serve as te starting point in developing entropy-cange relations for processes. e successful use of ds relations depends on te availability of property relations. Suc relations do not exist for a general pure substance but are available for incompressible substances (solids liquids) and ideal gases. e entropy-cange and isentropic relations for a process can be summarized as follos:. ure substances: Any process: s= s s Isentropic process: s = s. Incompressible substances (J/g K) Any process: s s = Cav ln (J/g K) Isentropic process: = 3. Ideal gases: a. Constant specific eats (approximate treatment): Any process: and s s C R v = vav ln + ln (J/g K) v s s = Cpav ln R ln (J/g K)

3 Or on a unit-mole basis and v s s = Cvav ln + Ruln (J/mol K) v s s = Cpav ln Ruln (J/mol K) Isentropic process: v = v s = const. = s = const. v = v s = const. b. Variable specific eats (exact treatment): Any process: ( )/ o o s s = s s Rln (J/g K) or o o s s = s s Ru ln (J/mol K) Isentropic process:

4 o o s = s + Rln (J/g K) v v = r s = const. r v = v r s = const. r ere r is te relative pressure and v r is te relative specific volume. e function s o depends on temperature only. e steady-flo or for a reversible process can be expressed in terms of te fluid properties as rev (J/g) = v d e pe For incompressible substances (v = constant) steady-flo or for a reversible process simplifies to = v ( rev ) e pe (J/g) e or done during a steady-flo process is proportional to te specific volume. erefore v sould be ept as small as possible during a compression process to minimize te or input and as large as possible during an expansion process to maximize te or output. e reversible or inputs to a compressor compressing an ideal gas from to in an isentropic (v = constant) polytropic (v n = constant) or isotermal (v = constant) manner are determined by integration for eac case it te folloing results: Isentropic: comp in ( )/ R( ) R = =

5 olytropic: comp in ( n )/ n nr( ) nr n n = = Isotermal: comp in = Rln (J/g) e or input to a compressor can be reduced by using multistage compression it intercooling. For maximum savings from te or input te pressure ratio across eac stage of te compressor must be te same. Most steady-flo devices operate under adiabatic conditions and te ideal process for tese devices is te isentropic process. e parameter tat describes o efficiently a device approximates a corresponding isentropic device is called isentropic or adiabatic efficiency. It is expressed for turbines compressors and nozzles as follos: η Actual turbine or Isentropic turbine or a = = s a s η C η N Isentropic compressor or Actual compressor or s = = Actual KE at nozzle exit r V a = = r Isentropic Ke at nozzle exit V s a s a a s In te relations above a and s are te entalpy values at te exit state for actual and isentropic processes respectively. e entropy balance for any system undergoing any process can be expressed in te general form as

6 Sin Sout + Sgen = Ssystem 443 { 3 Net entropy transfer Entropy Cange in by eat and mass generation entropy (J/K) e entropy balance for any system undergoing any process can be expressed in te general rate form as S& in S& out + S& gen = S& system 443 { 3 Rate of net entropy transfer Rate of entropy Rate of cange by eat and mass generation of entropy (W/K) For a general steady-flo process te entropy balance simplifies to S& = m& s ms & gen e e i i Q&

Entropy balance special forms. Quasiequilibrium (QE) process. QE process is reversible. dt Tk = = +

Entropy balance special forms. Quasiequilibrium (QE) process. QE process is reversible. dt Tk = = + Entropy balance Outline Closed systems Open systems Reversible steady flow wor Minimizing compressor wor Isentropic efficiencies Examples Entropy balance Sin Sout + Sgen = Ssys Entropy balance Entropy