# Finding Average Temperature Using Boltzman Constant

#### gspsaku

1. 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

2. Homework 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.

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#### TSny

Homework Helper
Gold Member
Check your conversion of units for the particle density.

#### gspsaku

Check your conversion of units for the particle density.
I've tried 1.01x10^2m^-3 and it was wrong as well

#### TSny

Homework Helper
Gold Member
The particle density is about 1 particle per cm3. How many cm3 are in 1 m3?

#### gspsaku

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?

#### TSny

Homework Helper
Gold Member
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.

#### gspsaku

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?

#### TSny

Homework Helper
Gold Member
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?

#### gspsaku

The particle density is about 1 particle per cm3. How many cm3 are in 1 m3?
1m^3 has 1.0x10^6cm^3

Yes, that's correct. So what wold be the conversion from cm-3 to m-3?
I think I'm going in circles man....

#### TSny

Homework Helper
Gold Member
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 ?

#### gspsaku

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 isnt correct. Have you tried to solve it yet?

#### TSny

Homework Helper
Gold Member
1.01x10^-6 but it isnt 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 ?

#### gspsaku

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

#### TSny

Homework Helper
Gold Member
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?

• gspsaku

#### gspsaku

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.

#### TSny

Homework Helper
Gold Member
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.)

• gspsaku

#### gspsaku

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

#### TSny

Homework Helper
Gold Member
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?

• gspsaku

#### gspsaku

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?

#### TSny

Homework Helper
Gold Member
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 .

• gspsaku

#### gspsaku

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

#### TSny

Homework Helper
Gold Member
You are welcome. Glad you got it. Sorry if at times I was confusing you more than helping.

• gspsaku

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