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Calculating pressure fromV1 to V2 with a polytropic exponent

  • Thread starter metiz1
  • Start date
  • #1
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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
 

Answers and Replies

  • #2
I like Serena
Homework Helper
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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
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Thank you for your reply.

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
I like Serena
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Thank you for your reply.

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:
[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
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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
I like Serena
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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
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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.
 

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