Finding Average Temperature Using Boltzman Constant

In summary: I don't know what was up with me. My brain just wasn't working. I'm sorry for the trouble. Have a good night!In summary, the conversation discusses the conversion of units for particle density in order to calculate the average temperature of mostly empty space. It is determined that there are 1.01 x 10^6 particles per m3, and this can be expressed as 1.01 x 10^6 m-3. This information is used to find the correct answer for the average temperature calculation.
  • #1
gspsaku
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Homework Statement


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

Homework Equations


T=P/pKb

The Attempt at a Solution


I plugged in (5.1x10^-17)/(1.01x10-9m^-3)(1.38x10^-23). Answer was incorrect.
 
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  • #2
Check your conversion of units for the particle density.
 
  • #3
TSny said:
Check your conversion of units for the particle density.
I've tried 1.01x10^2m^-3 and it was wrong as well
 
  • #4
The particle density is about 1 particle per cm3. How many cm3 are in 1 m3?
 
  • #5
TSny said:
The particle density is about 1 particle per cm3. How many cm3 are in 1 m3?
That's 1.0x10^-6

Because it's cm^-3, does that make change?
 
  • #6
gspsaku said:
That's 1.0x10^-6
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.
 
  • #7
TSny said:
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.
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?
 
  • #8
gspsaku said:
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?
Yes, that's correct. So what wold be the conversion from cm-3 to m-3?
 
  • #9
TSny said:
The particle density is about 1 particle per cm3. How many cm3 are in 1 m3?
1m^3 has 1.0x10^6cm^3

TSny said:
Yes, that's correct. So what wold be the conversion from cm-3 to m-3?
I think I'm going in circles man...
 
  • #10
gspsaku said:
1m^3 has 1.0x10^6cm^3
Yes. So if, on the average, there are 1.01 particles in each cm3, how many particles are in 1 m3 ?
 
  • #11
TSny said:
Yes. So if, on the average, there are 1.01 particles in each cm3, how many particles are in 1 m3 ?
1.01x10^-6 but it isn't correct. Have you tried to solve it yet?
 
  • #12
gspsaku said:
1.01x10^-6 but it isn't correct. Have you tried to solve it yet?
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 ?
 
  • #13
TSny said:
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 ?
1.0x10^6cm^3
 
  • #14
gspsaku said:
1.0x10^6cm^3
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?
 
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  • #15
TSny said:
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?
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.
 
  • #16
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.)
 
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  • #17
TSny said:
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.)
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
 
  • #18
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?
 
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  • #19
TSny said:
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?
Wouldn't it just be 1.01x106?
 
  • #20
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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  • #21
TSny said:
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 .
Thanks for your patience and help. Man, I always thought I was okay with my unit conversions but the m-3 really messed me up. Again, thank you for sticking through with me in this process. I was so close to just giving up as I got so frustrated because it wasn't something difficult but it felt like I was on some sort of advanced calc problem and it was just a simple conversion. Thank you, thank you, thank you
 
  • #22
You are welcome. Glad you got it. Sorry if at times I was confusing you more than helping.
 
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1. What is the Boltzmann constant?

The Boltzmann constant, denoted by k, is a physical constant that relates the average kinetic energy of particles in a gas to the temperature of the gas. It has a value of approximately 1.38 x 10^-23 joules per kelvin.

2. How is the Boltzmann constant used to find average temperature?

The Boltzmann constant can be used in the Boltzmann distribution, which describes the probability of particles having a certain amount of energy at a given temperature. By solving for temperature in this equation, we can find the average temperature of a system.

3. What are the units of the Boltzmann constant?

The Boltzmann constant has units of energy per temperature, specifically joules per kelvin. This reflects its role in relating energy and temperature in the Boltzmann distribution.

4. How is the Boltzmann constant related to the ideal gas law?

The ideal gas law, which describes the relationship between pressure, volume, and temperature of a gas, includes the Boltzmann constant in its formula. This constant helps to account for the behavior of individual gas particles in the overall system.

5. Why is the Boltzmann constant important in thermodynamics?

The Boltzmann constant plays a crucial role in thermodynamics because it allows us to relate the macroscopic properties of a system, such as temperature, to the microscopic behavior of individual particles. It also helps us to understand the thermal equilibrium and energy distribution within a system.

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