Finding Average Temperature Using Boltzman Constant

[gspsaku]

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.

 

[TSny]

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]

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]

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]

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]

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 isn't correct. Have you tried to solve it yet?

 

[TSny]

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 ?

 

[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]

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]

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]

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]

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]

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]

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]

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]

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]

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