# How do you calculate the density of a gas with temperature change?

Sep 26, 2014

The Ideal Gas Law can be stated as $P V = n R T$ where the symbols have their usual meanings. Write $n$ as $\frac{M}{M} _ 0$ where $M$ is the mass of the gas and ${M}_{0}$ is the molar mass.

$\setminus \iff P V = \left(\frac{M}{M} _ 0\right) R T$

$\setminus \iff P {M}_{0} = \left(\frac{M}{V}\right) R T$

$\setminus \iff P {M}_{0} = \mathrm{dR} T$

$\setminus \iff d = \frac{P {M}_{0}}{R T} \setminus \propto \frac{P}{T}$

Use the above equation to calculate the density of a gas with temperature change.

This has many implications that should be easy to understand.

• Density is directly proportional to pressure because high pressure results in compression of a gas, meaning that you have a chunk of gas in a less amount of space, meaning higher density.

• Density is inversely proportional to temperature because increasing temperature always causes the decompression of particles.