1. ## Re-arranging an equation.

Need help with a question guys, any help will be most appreciated.

The pressure, p, and volume, V, of a gas undergoing a polytropic process are related by the equation:

p1V1n = p2V2n

where n is the polytropic index.

If p1V1/ T1 = p2V2/ T2

determine and expression for p1 in terms of p2 , T1, T2 and n

It has got me a bit stumped guys so any help would be most appreciated.

Thanks

2. The pressure, p, and volume, V, of a gas undergoing a polytropic process are related by the equation:

p1V1n = p2V2n

where n is the polytropic index.

Ifp1V1/ T1 = p2V2/ T2

determine and expression for p1 in terms of p2 , T1, T2 and n
From the last equation, $\displaystyle p_1=p_2\frac{T_1}{T_2}\frac{V_2}{V_1}$, so we have to find $\displaystyle\frac{V_2}{V_1}$. From the first equation, $\displaystyle\left(\frac{V_2}{V_1}\right)^n=\frac{ p_1}{p_2}$. By taking root of degree n of both sides, you can find $V_2/V_1$.

A remark concerning notation. As is standard, use * for multiplication (it can be omitted in certain cases like 3x) and ^ for exponentiation. Otherwise, it is not clear if your p1V1n means $p_1V_1n$ or $p_1V_1^n$.

Dear Dan Brown,
I assume you have a chemistry problem and cannot get into the Chemistry Forum. If you describe your problem I will try to help

bjh

4. so does V2/V1=(p1/p2)^1/n

and

p1 = p2T1/T2*(p1/p2)^1/n

5. Yes.

6. Therefore
p1 = (p2T1p1^1/n)/T2p2^1/n

If I divide by p1^1/n

P1/P1^1/n = p2T1/T2p2^1/n

This is were i'm stuck

7. This is were i'm stuck
What are you trying to do? The original problem was to "determine an expression for p1 in terms of p2 , T1, T2 and n". This has been done in post #4.

8. but i still have p1 on both sides of the equation, i need to make p1 the subject

9. Sorry, you are right, of course.

So, we have $\displaystyle\frac{p_1}{p_1^{1/n}}=\frac{p_2}{p_2^{1/n}}\frac{T_1}{T_2}$, i.e., $\displaystyle p_1^{(n-1)/n}=p_2^{(n-1)/n)}\frac{T_1}{T_2}$. Raising both sides to n/(n-1), we get $\displaystyle p_1=p_2\left(\frac{T_1}{T_2}\right)^{n/(n-1)}$.

10. ## rearanging an equation

PV^n = constant is used to calculate one unknown.polytropic process n=1.395
P1V1/T1 = P2V2/T2 is used to calculate a temperature
Example V1=12.48 cu ft V2=5.0 cu ft V1@ 70 F
P1 = 14.7 psia P2 = 52.6psia t=301F

bjh

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### (p1/p2)^n-1 = T1/T2 solve for n

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