Finding pressure and temperature of helium gas from volume and atom count

[shyguy79]

Homework Statement

Find the pressure and temperature when given the following data on helium gas:

Volume (V) = 0.10 m^3 ** Helium mass (m) = 4.0 amu ** Number of atoms (N) = 3.0 x 10^24

Assuming PV = 1 then P=1/V then Pressure = 1.0 / 0.10m^3 = 10Pa

Homework Equations

PV = NkT arranged for T = PV/Nk OR PV = nRT arranged for T = PV/nR

The Attempt at a Solution

Mm = Mr x 10-3 = 4.0 x 10-3 so the mass is 4.0 x 10^-3 / 6.02 x 1023 = 6.6 x 10^-27

The temperature T is then:
T = PV/Nk
T = P x 0.10m^3 / 3.0 × 10^24 mol−1 x 1.381 × 10^−23 J K−1

But I have no idea how to get Pressure - I've tried using Boyles law PV = constant but get lost

Any pointers would be deeply appreciated

 

[NascentOxygen]

One mole of an ideal gas will occupy a volume of 22.4 liters at STP (Standard Temperature and Pressure, 0°C and one atmosphere pressure).

Though I think you still are lacking some information.

 

[shyguy79]

One mole of an ideal gas will occupy a volume of 22.4 liters at STP (Standard Temperature and Pressure, 0°C and one atmosphere pressure).

Though I think you still are lacking some information.

Thanks for the reply, that's all I've been given - been told Charles Law and Botles Law may come in handy but don't know how!?

 

[NascentOxygen]

Charles' and Boyle's Laws are just special cases of the general gas law.

You are looking at: $PV \div T$ = constant
but I think you can only find the quotient $P \div T$

 

[technician]

You are given the number of atoms = 3 x 10^24 which = 5moles (n)
If you substitute this into PV = nRT you can get T but the answer is not sensible ?
I can't see why you have been given the mass of He atom = 4 amu !

 

[gneill]

You are given the number of atoms = 3 x 10^24 which = 5moles (n)
If you substitute this into PV = nRT you can get T but the answer is not sensible ?
I can't see why you have been given the mass of He atom = 4 amu !

It's possible that one might have to resort to the isentropic relationships for an ideal gas.

 

[technician]

I think I have just realized that shyguy is assuming that PV=1... it is not a given in the question...I don't know any more to add!

 

[shyguy79]

Yes, but working out the math the pressure would be 10 Pascals and the Temperature would 0.0012 Kelvin - and that make hardly any sense!

 

[NascentOxygen]

Yes, but working out the math the pressure would be 10 Pascals and the Temperature would 0.0012 Kelvin - and that make hardly any sense!

Does your textbook provide the answer to this?

 

[shyguy79]

No, it's an assignment question but reading through the full wording it appears that the peak velocity is 1100m/s

 

[NascentOxygen]

No, it's an assignment question but reading through the full wording it appears that the peak velocity is 1100m/s

Is it really late at night where you are?

Velocity does not enter into the question. Well, only tangentially.

 

[mullac phie]

try this thread, very very similar,

https://www.physicsforums.com/showthread.php?t=370456

everything you need!

 

[shyguy79]

Thank you! Just what I was looking for!