Thermodynamic question involving work

[Liquidxlax]

Homework Statement

Show that the work done by a reversible function from P₁V₁ to P₂V₂ is

W = (P₁V₁ -P₂V₂)/ (x - 1)

using the relation PV^x = C where X and C are constants

Homework Equations

dW = PdV

The Attempt at a Solution

I'm going to have to update this more when i get home because i forgot my textbook and notebook

Basically what I did was draw a graph from P₁V₁ to P₂V₂ and the whole point is to find the area underneath the curve


My problem is I'm not sure how to include the change in pressure and the change in volume in this integral.

I'm basically getting (x-y)/xy where x and y are different volumes

Like i said i will update my work when i get home, but any help for now will be appreciated

 

[pabloenigma]

dw =PdV,there you are.
So to compute work,all you need to do is compute the definite integral of PdV from V₁ to V₂.
Express P in terms of V,by using the equation PV^x=constant(say k),ie P=kV^-x

Now Integrate KV^-x from V₁ toV₂,and you are done,provided you put the limits nicely(substitute k=P₁V₁^x in the 2nd term and k=P₂V₂^x in the first term)

 

[Liquidxlax]

dw =PdV,there you are.
So to compute work,all you need to do is compute the definite integral of PdV from V₁ to V₂.
Express P in terms of V,by using the equation PV^x=constant(say k),ie P=kV^-x

Now Integrate KV^-x from V₁ toV₂,and you are done,provided you put the limits nicely(substitute k=P₁V₁^x in the 2nd term and k=P₂V₂^x in the first term)

funny thing is that if you are right i did that, and i guess i must have messed up my algebra. Curse the few first days of school

 

[Liquidxlax]

dw =PdV,there you are.
So to compute work,all you need to do is compute the definite integral of PdV from V₁ to V₂.
Express P in terms of V,by using the equation PV^x=constant(say k),ie P=kV^-x

Now Integrate KV^-x from V₁ toV₂,and you are done,provided you put the limits nicely(substitute k=P₁V₁^x in the 2nd term and k=P₂V₂^x in the first term)

I did do that, but do you justify that k=P₂V₂^x=P₁V₁^x?

 

[pabloenigma]

In your question, PV^x=constant is the equation of the process,ie this equation characterizes and defines the process the system is made to go through.This defines the way P and V of the system changes. So, P and V of the system always saties this equation. If P₁V₁, P₂V₂,P₃V₃ , etc are pressure and volume of the system in different points of time, then for all thes states, P_iV_i=k is satisfied.

So from the initial and final states we get

P₁V₁= P₂V[/SUB]2[/SUB]=k.
Got it?