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

 

[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.

 

[metiz1]

Thank you for your reply.

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

 

[I like Serena]

Thank you for your reply.

I can't say I really 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? )

 

[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

 

[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...

 

[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.