# Calculating pressure fromV1 to V2 with a polytropic exponent

1. Nov 6, 2011

### metiz1

1. The problem statement, all variables and given/known data

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

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

3. The attempt at a solution

non

2. Nov 6, 2011

### I like Serena

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.

3. Nov 6, 2011

### 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?

4. Nov 6, 2011

### I like Serena

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? )

5. Nov 6, 2011

### 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

6. Nov 6, 2011

### I like Serena

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...

7. Nov 6, 2011

### 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.