Calculating pressure fromV1 to V2 with a polytropic exponent

In summary, Homework Equations state that the final pressure is equal to the initial pressure multiplied by 7 over 5.
  • #1
metiz1
4
0

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
 
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  • #2
Welcome to PF, metiz1! :smile:

An adiabatic process (for an ideal gas) has [itex]P V^\gamma = constant[/itex], where [itex]\gamma = {7 \over 5}[/itex] for air (as a diatomic ideal gas).
Combined with the initial pressure as standard pressure, you can calculate the final pressure.
 
  • #3
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?
 
  • #4
metiz1 said:
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:
[tex]P_{initial} (V_{initial})^{7 \over 5} = P_{final} (V_{final})^{7 \over 5}[/tex]

Solve for [itex]P_{final}[/itex].


You can find the formula for instance here:
http://en.wikipedia.org/wiki/Adiabatic_process
(Shouldn't it be in your notes or something? :confused:)
 
  • #5
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
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
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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