# Homework Help: Entropy in polytropic processes

1. Aug 24, 2013

### nvjnj

1. The problem statement, all variables and given/known data

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. Aug 24, 2013

### SteamKing

Staff Emeritus
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.

3. Aug 26, 2013

### nvjnj

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)