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Entropy in polytropic processes

  1. Aug 24, 2013 #1
    1. The problem statement, all variables and given/known data

    I have question on entropy for which I have no idea about, please help me out...

    a) Change of entropy of a gas is given with usual notations by:
    s2-s1=cvln(T2/T1)+Rln(V2/V1)

    using this relationship, show that for a polytropic process, entropy change can be expressed as:
    s2-s1=cv(n-k/n-1)ln(T2/T1)

    b) In an air turbine air expands from 7bar and 460°C to 1.012bar and 160°C. This process can be assumed as a polytropic process. Determine,

    1) Whether the flow is reversible or irreversible
    2) The net entropy change per unit mass of air.


    Please give me a step wise calculation on how to arrive at the answers 'cos I'm so weak in entropy. Additionally I would appreciate if someone can give me links for a site where I can bring my entropy knowledge up to level 'cos, even though I understand the Clausis inequality and the derivation of entropy property, I'm at a loss on how to apply it in a question such as this....

    2. Relevant equations

    No idea

    3. The attempt at a solution

    No idea
     
  2. jcsd
  3. Aug 24, 2013 #2

    SteamKing

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    Sorry, PF is not a homework service. You'll have to develop your own calculations. We can examine your work and give you suggestions if it needs correction or improvement.
     
  4. Aug 26, 2013 #3

    Ok, here is an attempt at the question...

    Let s2-s1=cvln(T2/T1)+Rln(V2/V1)----------(1)


    Polytropic Process : PVk=c
    rearranging and substituting gives : V2/V1=(T2/T1)(-1/k-1)

    Substituting to (1) gives; s2-s1=cvln(T2/T1)+Rln(T2/T1)(-1/k-1)

    Rearranging and simplifying : s2-s1=cvln(T2/T1)-(R/k-1)ln(T2/T1)-----------------------(2)

    Using the relationship : cp=cv+R
    rearranging : (cp/cv)=1+(R/cv)
    which gives : k-1=(R/cv)---->cv(k-1)=R---------------(3)

    Substituting (3) to (2) gives :
    s2-s1=cvln(T2/T1)-(cv/k-1)(k-1)ln(T2/T1)

    Which gives me s2-s1=0 ......which is not what I need!! Please help me out....
     
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