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Ideal Gas Law Volume Problem

  1. Apr 21, 2014 #1
    1. The problem statement, all variables and given/known data

    Here is the problem: You are worried that your -80C freezer is on the fritz. Unfortunately you do not have a thermometer. You do have a balloon. so, you blow up the balloon and measure that it has a diameter of 10cm when at 25C. you put it in the freezer, let it come to thermal equilibrium, and measure the new volume to be 9cm. What is the temperature of the freezer? (assume the balloon is a perfect sphere).

    A) -55C
    B) -66C
    C) -77C
    D) -88C

    2. Relevant equations

    I'm really not sure how do solve this with the given information. I am also unsure if the "new volume" is a typo and is actually supposed to be new diameter since the cm are not cubed.

    3. The attempt at a solution

    I've tried putting numbers in the equation P1V1/T1=P2V2/T2 but never been able to come out with any of those answers.
     
  2. jcsd
  3. Apr 21, 2014 #2
    Did you remember to use absolute temperature? As far as the diameter issue is concerned, try it both ways and see if you match any of the answers.

    Chet
     
  4. Apr 21, 2014 #3
    What about the pressure calculation? It seems like there are too many variables missing to solve P1V1/T1=P2V2/T2. Is there a way to calculate the pressure of the balloon before it is in the freezer? I know the equation PV=nRT but n is unknown as well. Also, even if P1 can be calculated that still leaves two variables left. We did examples in lecture where only one variable was missing which is why this problem is more confusing. Am I missing some conceptual understanding of the problem where pressure isn't need or can be canceled out?
     
  5. Apr 21, 2014 #4
    The pressure is assumed to stay constant at 1 atm.

    Chet
     
  6. Apr 21, 2014 #5
    What are the assumptions behind the ideal gas approximation? Does it matter whether the gas is air, N2, CO2 , He etc.?
     
  7. Apr 21, 2014 #6
    The pressure is low enough.
    No. Only the range of applicability.

    Chet
     
  8. Apr 21, 2014 #7
    Using 9 as the diameter I was able to get -55 C as an answer. Does that sound right to you? Thank you for your help.
     
  9. Apr 21, 2014 #8
    I get -56 C, but who's counting.

    Chet
     
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