Derive the seven general property equation of the following thermodynamics processes:a. POLYTROPIC PROCESS 5. Polytropic ProcessPolytropic process is an internally reversible process. Thefrom process definition:previous four (4) processes discussed above is also a polytropicPV" = C where n = any positive real number (n # k,1, and ∞.)PV" = CP = CV-"process with various polytropic coefficient 'n'. Now, we define aspecial case of polytropic process wherein ´n' is any positive realnumber and n + k, 1, and . Thus also, we may have concludedsubstituting to the integral and evaluating:that Q + 0 also. And, as derived using the seven (7) generalA-[V1-nPV= CV-"dV = C= PVnequations, we have:- nv Any Process relation:P2V2-P¡V1 _ mR(T2 – T1)Wn =1-n1-nPV= CP;V _ P¿V2T2Internal Energy:=Following the relation in the change in internal energy, we haveThe relation between these three (3) parameters can bean internal energy of:simplifiedAU = mC,(T2 – T1)further to determine the relation between any of the twov Heat Transferred:desiredFollowing the relation of heat transfer, we have:parameters using:Q = AU + W,mR(T2 – T,)PV" = C where n = any positive real number (n # k,1, and co.)Q = mC,(T2 – T;) +1-nPV™ = CFrom properties of ideal gas, we have:Deriving the pressure - volume relation:P,V," = P,V2"Cyk -; R = C„(k – 1)一Substituting from the above equation, we have:mC, (k – 1)(T2 – T,)Q = mC,(T2 – T1) +Also to derive 'n', we may use:1-n(k -= mc,(T, – T,) 1 + = mC,(T, – T,)In=n In1-nNote that the relation of heat transferred under polytropicInprocess has a special value for specific heat. That is the specificInheat under polytropic process, Cn, with an equivalent below:Deriving the volume – temperature relation:Cn = C,;n# 1; fromPVrelationshipAnd heat transferred under polytropic process will be:Substituting to the previously derived pressure- volumeQ = mC„(T2 – T,)relation:V Enthalpy:Following the relation in the change in enthalpy, we have anenthalpy of:開AH = mC,(Tz – T,)V Entropy:Deriving the pressure – temperature relation:Following the guiding equation as represented by the to obtainPV; from relationshipAS,Substituting the previously derived volume - temperaturedQmCndTAS =Trelation:Evaluating the integral, we will have:n-1原-“n-1AS = mC„ln1-nNote that the other equivalent of T2/T; can be used also todetermine the value of AS. That is,Simplifying, we will have:n-1一”n-1開-v Work Non-flow:Applying the integral to evaluate the work non-flow of the idealgas under polytropic process, we will again employ the use of:v Work Steady flow:W. = [° ravPdVFor work steady flow, we follow the integral below:W = -VdPfrom process definition:PV" = C where n = any positive real number (n # k,1, and ∞.)PV" = CVsubstituting to the integral and evaluating in below:= -1-nSimplifying further we will arrive for the relation:P,Vz-P,V,= nmR(T, – T,)1-nW, = n1-nTherefore, at polytropic process, we have a work on steady flowsystem as:w, = nW, = nPdV

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Answered: seven general property equation of the…

Engineering

Mechanical Engineering

seven general property equation of the following thermodynamics processes: a. POLYTROPIC

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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