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Is it possible to calculate the mass of gas remaining in a cylinder simply by measuring temperature and pressure?

Physics Asked on January 18, 2021

Given $pV=nRT$, where;

$p$ = Pressure, $V$ = Volume, $n$ = Number of moles of gas, $R$ = Gas constant and $T$ = Temperature in Kelvin.

Also, the mass can be calculated by;

$m = nM rightarrow n = frac{m}{M}$, where;

$m$ = mass, $n$ = Number of moles and $M$ = Relative molecular mass.

Putting these two equations together, I get;

$pV = frac{mRT}{M} rightarrow m = frac{pVM}{RT}$.

Therefore I assume that as you release gas from that cylinder, you can calculate the mass of gas remaining in the cylinder simply by taking readings of the temperature and pressure in the cylinder.

Of course, this is assuming you know the volume of the cylinder, as well as it having just one gas, so you know the Relative atomic mass too.

Is this correct?

One Answer

You're quite right, at least you are if you take M to be the relative molecular mass. [The molecules of many gases, including oxygen, nitrogen and hydrogen, consist of more than one atom, bonded together.]

Answered by Philip Wood on January 18, 2021

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