Entropy in polytropic processes

[nvjnj]

Homework Statement

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...

Homework Equations

No idea

The Attempt at a Solution

No idea

 

[SteamKing]

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.

 

[nvjnj]

Homework Statement

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...

Homework Equations

No idea

The Attempt at a Solution

No idea

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

Let s2-s1=cvln(T₂/T₁)+Rln(V₂/V₁)----------(1)Polytropic Process : PV^k=c
rearranging and substituting gives : V₂/V₁=(T2/T1)^(-1/k-1)

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

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

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

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

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