# Calculating pressure fromV1 to V2 with a polytropic exponent

metiz1

## 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

## The Attempt at a Solution

non

Homework Helper
MHB
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.

metiz1

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?

Homework Helper
MHB

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:
(Shouldn't it be in your notes or something? )

metiz1
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

Homework Helper
MHB
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...

metiz1
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.