# 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: