# Calculating pressure fromV1 to V2 with a polytropic exponent

## Homework Statement

I have a bicycle pump where I need to calculate the pressure in a certain volume. No heat is lost during compression so this is a isentropic system

initial volume is 0.3L
final volume is 0.0195
Gas is air
n=k

## Homework Equations

I don't know, that's the problem. I recognise this as a fairly simple question but I just don't know

non

## Answers and Replies

I like Serena
Homework Helper
Welcome to PF, metiz1! An adiabatic process (for an ideal gas) has $P V^\gamma = constant$, where $\gamma = {7 \over 5}$ for air (as a diatomic ideal gas).
Combined with the initial pressure as standard pressure, you can calculate the final pressure.

Thank you for your reply.

I can't say I realy understand your reply though...Shouldn't I enter the initial temperature (lets say 20C, 293K) somewhere in the equation?

I like Serena
Homework Helper
Thank you for your reply.

I can't say I realy understand your reply though...Shouldn't I enter the initial temperature (lets say 20C, 293K) somewhere in the equation?

No, you don't need the temperature.

Let me rephrase:
$$P_{initial} (V_{initial})^{7 \over 5} = P_{final} (V_{final})^{7 \over 5}$$

Solve for $P_{final}$.

You can find the formula for instance here:
http://en.wikipedia.org/wiki/Adiabatic_process
(Shouldn't it be in your notes or something? )

Thanks for your help! I had to use a hypotetical situation (n=1.4) for my calculations and see how the real word measurements stacked up....The n value I got was like 0.8....I dun goofed the measurement I think :P

I like Serena
Homework Helper
Hmm, I just realized... you're talking about a pump.
I suppose that means the amount of air changes?
Kind of relevant, since the formula only works when the amount of air remains constant...

Yes you are right, however, in this situation I had to asume all the air was being compressed in a smaller volume withouth any air or heat escaping, so all is good.