# Pressure and Temperature question: Ideal Gas Laws

## 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 - Ive tried using Boyles law PV = constant but get lost

Any pointers would be deeply appreciated

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NascentOxygen
Staff Emeritus
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.

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
Staff Emeritus
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 $P \div T$

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
Mentor
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.

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

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
Staff Emeritus
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!

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

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