# Gas Laws -- why calculate the mean square speed at 273K?

Faiq

## Homework Statement

Why is the formula ##p = \frac{1}{3}\rho<c^2>## used to calculate the mean square speed at 273K?
Why 273K?

Homework Helper
It works at any temperature. Could you give a bit more context ? Is this a section in your textbook you have a question about or is it in an exercise ?

Faiq
The density of a gas at a temperature of ##273~K## and a pressure of ##1.02*10^5~ Pa## is ##0.9kgm^{-3}##. It may be asssumed to be an ideal gas.
Calculate rms speed at 273K and 546K.

For 273, we were supposed to use the given equation and for second we were supposed to used the ratio of mean square speed and temperature.
My thinking is the equation only applies for those temperature for which we are using the pressure values.

Mentor
You are given pressure and density at 273 K and asked to calculate rms at exactly this temperature, I don't see where is the problem?

Faiq
You are given pressure and density at 273 K and asked to calculate rms at exactly this temperature, I don't see where is the problem?
The confusion I had was why is that formula only applicable for the 273K. That's to say why I can't just put that value down for 546K? Later I realized, the pressure inserted in those equations are the indicator of what temperature should the RMS value be for.

Homework Helper
We're still missing context. Please be a bit more complete in formulating problem statements. This way we spend way too much time dragging out what is troubling you.

Missing:

## The Attempt at a Solution

Accidentally ? Or did you erase them ? That's a no-no in PF !

And anyway, 1. should probably have been
The density of a gas at a temperature of ##273~K## and a pressure of ##1.02*10^5~ Pa## is ##0.9kgm^{-3}##. It may be asssumed to be an ideal gas.
Calculate rms speed at 273K and 546K.
Any word or sentence missing from this full problem statement ? If no, then a list of all variables is good to have at hand. For you too.
For 273, we were supposed to use the given equation and for second we were supposed to used the ratio of mean square speed and temperature.
What given equation ?

Did you do anything at all with the information that the gas can be considered an ideal gas ?

Where did the
formula ##p = \frac{1}{3}\rho<c^2>##
come from ? From the textbook or from the problem statement ? (or perhaps from the solution manual ?)

Faiq
1. No words or sentences are missing.
2. The given equation is ##p = \frac{1}{3}\rho<c^2>##
3. By telling us that it could be considered an ideal gas, permission was given to use the ideal gas law and the provided equation.
4. The formula was supposed to be derived by using the equation ##pV = \frac{1}{3}Nm<c^2>## and ##\rho = \frac{Nm}{V}##

Btw my confusion has been sorted out. Thanks for the help though

• BvU