Finding area from work, pressure and volume

[JoeyBob]

Homework Statement

see attached

Relevant Equations

W=integral(PdV)

So I basically took the integral and ended up with W=PVf-A(Vf^3)/3-PVi+A(Vf^3)/3

so 65.7=72*5.3-A(5.3)^3/3-72(2.4)+A(2.4)^3/3

But when I solve for A I get the wrong answer of 3.179 when the answer is suppose to be 5.05. I've checked my calculation with an algebra calculator too...

 

[haruspex]

Homework Statement:: see attached
Relevant Equations:: W=integral(PdV)

So I basically took the integral and ended up with W=PVf-A(Vf^3)/3-PVi+A(Vf^3)/3

so 65.7=72*5.3-A(5.3)^3/3-72(2.4)+A(2.4)^3/3

But when I solve for A I get the wrong answer of 3.179 when the answer is suppose to be 5.05. I've checked my calculation with an algebra calculator too...

You seem to have mixed up P₀ and P₁.

 

[JoeyBob]

You seem to have mixed up P₀ and P₁.

Wait wouldn't tha mean there's two unknowns then? How would I find P0?

 

[haruspex]

Wait wouldn't tha mean there's two unknowns then? How would I find P0?

You have two equations relating P₀, P₁, P₂, V₁, V₂ and A.

 

[JoeyBob]

You have two equations relating P₀, P₁, P₂, V₁, V₂ and A.

Wait so is it P1=P0+AV and then the integral eqn?

 

[haruspex]

Wait so is it P1=P0+AV and then the integral eqn?

No.
You are given P=P₀-AV² as a general fact. In particular this will be true at the initial and final states. Plug in the values/variables for those states to get two equations.

 

[Chestermiller]

You have $$P_1=P_0-AV_1^2$$ so $$P_0=P_1+AV_1^2$$So you can eliminate ##P_0##

 

[haruspex]

Well the problem statement says: $$P=P_0-AV^2$$so at the initial condition, $$P_1=P_0-AV_1^2$$So my algebra tells me that $$P_0=P_1+AV_1^2$$
What am I missing?

Sorry, I read what I was expecting, not what you wrote.
I read your second line as $$P_2=P_0+AV_2^2$$, reinforced by your comment about eliminating P₀. So what I should have written is $$P_2=P_0-AV_2^2$$.

 

[Chestermiller]

Sorry, I read what I was expecting, not what you wrote.
I read your second line as $$P_2=P_0+AV_2^2$$, reinforced by your comment about eliminating P₀. So what I should have written is $$P_2=P_0-AV_2^2$$.

What do you need to know P2 for?

 

[haruspex]

What do you need to know P2 for?

I'm not saying you do. I'm explaining what I thought you had written and what I thought you had intended.