# Thermodynamics-boundary work

1. Feb 16, 2015

### tsukuba

1. The problem statement, all variables and given/known data
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
2. Relevant equations
PVn=constant
I was thinking I would have to use log to figure out n maybe?

3. The attempt at a solution
haven't been able to work it out backwards. Need your help please!

2. Feb 16, 2015

### Andrew Mason

If xn = k then ln(xn) = ln(k)

AM

3. Feb 16, 2015

### tsukuba

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

4. Feb 16, 2015

### tsukuba

somebody helpppp
I have a test tomorrow

5. Feb 16, 2015

### 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)

6. Feb 17, 2015

### Andrew Mason

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

Can you work it out from there?

AM