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Homework Help: Ideal gas pressure reduction

  1. Jul 21, 2007 #1
    1. The problem statement, all variables and given/known data
    an ideal gas is allowed to expand adiabatically until its volume increases by 50%. By what factor is the pressured reduced?(gamma=5/3)


    2. Relevant equations

    P1V1^gamma=P2V2^gamma

    3. The attempt at a solution

    P1V1^gamma=P2V2^gamma

    v2=v1+.5V1=3/2V1

    (p1/P2)=(v2/v1)^gamma=(3/2v1/v1)^gamma=3/2^gamma

    so P2=P1/(3/2)^gamma=0.51P1 sp P2=.5P1

    so reduced by approximately factor of 2

    This is actually the correct answer, but i dont understand the why the intial setup of the calculation, is P1/P2=(V2/V1)^gamma, the problem is looking for the reduction of the pressure, could someone explain why your suppose to set up calculation this way?
     
  2. jcsd
  3. Jul 21, 2007 #2
    more specifically why do you put p1 over p2 (p1/p2) equal to v2 over v1 (v2/v1) in solving this problem?
     
  4. Jul 21, 2007 #3

    Andrew Mason

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    Science Advisor
    Homework Helper

    ?? It is just algebra:

    [tex]P_1V_1^\gamma = K = P_2V_2^\gamma[/tex]

    [tex]\frac{P_1V_1^\gamma}{P_2} = V_2^\gamma[/tex]

    [tex]\frac{P_1}{P_2} = \frac{V_2^\gamma}{V_1^\gamma}= \left(\frac{V_2}{V_1}\right)^\gamma[/tex]

    AM
     
  5. Jul 21, 2007 #4
    lol for some reason i thought something else was going on, thanks anyways:biggrin:
     
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