AZING!What is the Polytopic Index for a given set of Pressure and Volume values?

[tsukuba]

Homework Statement

Hello, I came across a problem where the polytropic index is not given but I've been given P₁, P₂, V₁ and V₂.

P₁V₁ = P₂V₂ (130kPa)(0.007m³)ⁿ = (100kPa)(0.08637m³)ⁿ ----> n=1.249

Homework Equations

PVⁿ=constant
I was thinking I would have to use log to figure out n maybe?

The Attempt at a Solution

haven't been able to work it out backwards. Need your help please!

 

[Andrew Mason]

I was thinking I would have to use log to figure out n maybe?

If xⁿ = k then ln(xⁿ) = ln(k)AM

 

[tsukuba]

the value of n is not given. I just put it there because but what if it was
xⁿ = ?
solving for n

 

[tsukuba]

somebody helpppp
I have a test tomorrow

 

[tsukuba]

I came to this but now I am not sure how to isolate for n

ln(130) n*ln(0.07) = ln(100) n*ln90.08637)

 

[Andrew Mason]

I came to this but now I am not sure how to isolate for n

ln(130) n*ln(0.07) = ln(100) n*ln90.08637)

$$P_1V_1^n = P_2V_2^n$$
$$\frac{P_1}{P_2} = \left(\frac{V_2}{V_1}\right)^n$$
$$\ln(P_1)-\ln(P_2) = n(\ln(V_2) - \ln(V_1))$$

Can you work it out from there?

AM