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Finding Average Temperature Using Boltzman Constant

  1. Nov 12, 2016 #1
    1. The problem statement, all variables and given/known data
    Deep in space, there is a particle density, p, is 1.01cm^-3. Pressure is extremely low, P, is 5.1 x 10^-17 N/m^2. What is the average temperature of mostly empty space? Answer in K

    2. Relevant equations
    T=P/pKb

    3. The attempt at a solution
    I plugged in (5.1x10^-17)/(1.01x10-9m^-3)(1.38x10^-23). Answer was incorrect.
     
  2. jcsd
  3. Nov 13, 2016 #2

    TSny

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    Check your conversion of units for the particle density.
     
  4. Nov 13, 2016 #3
    I've tried 1.01x10^2m^-3 and it was wrong as well
     
  5. Nov 13, 2016 #4

    TSny

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    The particle density is about 1 particle per cm3. How many cm3 are in 1 m3?
     
  6. Nov 13, 2016 #5
    That's 1.0x10^-6

    Because it's cm^-3, does that make change?
     
  7. Nov 13, 2016 #6

    TSny

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    1.0 x 10-6 is a number much less than 1. But shouldn't there be a lot of cubic centimeters in one cubic meter? Try to visualize it.
     
  8. Nov 13, 2016 #7
    Okay, I must be doing something wrong.

    1cm = 1.0x10^-2 m
    1cm^2 = 1x10^-4 m^2
    1cm^3 = 1x10^-6 m^3

    Is this not correct?
     
  9. Nov 13, 2016 #8

    TSny

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    Yes, that's correct. So what wold be the conversion from cm-3 to m-3?
     
  10. Nov 13, 2016 #9
    1m^3 has 1.0x10^6cm^3

    I think I'm going in circles man....
     
  11. Nov 13, 2016 #10

    TSny

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    Yes. So if, on the average, there are 1.01 particles in each cm3, how many particles are in 1 m3 ?
     
  12. Nov 13, 2016 #11
    1.01x10^-6 but it isnt correct. Have you tried to solve it yet?
     
  13. Nov 13, 2016 #12

    TSny

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    In post #9 you correctly stated that 1 m3 has 1.0 x 106 cm3. So there are a million cm3 in 1 m3.

    You are given that the particle density is 1.01 cm-3. That means there are 1.01 particles per cm3. That is, there are 1.01 particles in one cm3. You want to convert that to how many particles are in one m3. Using the fact that 1 m3 has a million cm3, how many particles would be in 1 m3 ?
     
  14. Nov 13, 2016 #13
    1.0x10^6cm^3
     
  15. Nov 13, 2016 #14

    TSny

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    Why the units cm3 ? The question was how many particles are in one cubic meter?

    How would you answer the following?
    You know there are 1.01 particles in each cm3 of space. So, how many particles are in 2 cm3 of space?
     
  16. Nov 13, 2016 #15
    I'm sorry, there is a disconnect here. I don't get it and all I am doing is spinning my wheels. I appreciate the attempt and patience at trying to help me with this but it's obvious I don't get it. I assume once the professor shows us the answer, I'll get it.
     
  17. Nov 13, 2016 #16

    TSny

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    OK. It might be the way I'm trying to get you to see it that's not working. I think it's similar to the following.

    If I told you that on the average each house in a certain town has 3 people inside and if there are 1000 houses in the town, then how many people are inside houses in this town?

    Likewise, if each cm3 of space has 1.01 particles and if you have a volume that contains 1 million cm3, then how many particle do you have?
    (Think of each cm3 as a little cube. A volume of 1 m3 contains a million of these little cubes.)
     
  18. Nov 13, 2016 #17
    Okay, I will continue to try and work this out.

    If each cm3 of space has 1.01 particles and we have 1 million cm3, that means I have 1,010,000 particles
     
  19. Nov 13, 2016 #18

    TSny

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    Yes. Good. You have 1,010,000 particles in 1 m3. Or, you can express it as 1.01 x 106 particles in 1 m3.

    So, what is the particle density, p, in particles per m3?
     
  20. Nov 13, 2016 #19
    Wouldn't it just be 1.01x106?
     
  21. Nov 13, 2016 #20

    TSny

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    Yes. That's right. So, p = 1.01 x 106 particles per m3. This may be written as p = 1.01 x 106 m-3 .
     
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