# Calculating pressure fromV1 to V2 with a polytropic exponent

• metiz1
In summary, Homework Equations state that the final pressure is equal to the initial pressure multiplied by 7 over 5.
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

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.

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?

metiz1 said:

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:
(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

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.

## 1. What is the formula for calculating pressure from V1 to V2 with a polytropic exponent?

The formula is P2/P1 = (V1/V2)n, where P1 is the initial pressure, P2 is the final pressure, V1 is the initial volume, V2 is the final volume, and n is the polytropic exponent.

## 2. How do you determine the polytropic exponent for a given system?

The polytropic exponent, n, is determined by the type of process or expansion that the system undergoes. For example, for an isothermal process, n is equal to 1. For an adiabatic process, n is equal to the ratio of specific heats, γ.

## 3. Can the polytropic exponent be negative?

Yes, the polytropic exponent can be negative. This indicates that the process is a compression rather than an expansion. In this case, the pressure decreases as the volume decreases.

## 4. How do you interpret the value of the polytropic exponent in the pressure-volume relationship?

The value of the polytropic exponent determines the shape of the pressure-volume curve. A value of n=1 indicates an isothermal process, n>1 indicates a process with increasing pressure as volume decreases, and n<1 indicates a process with decreasing pressure as volume decreases.

## 5. What are the limitations of using the polytropic exponent to calculate pressure from V1 to V2?

The polytropic exponent assumes a specific type of process or expansion, which may not accurately represent real-world systems. It also does not account for factors such as external forces or energy losses, which can affect the results.

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