# Ideal gas law

The Ideal Gas Law is a law of physics, specifically thermodynamics, which describes the properties of an ideal gas.

## The Law

The ideal gas law unifies Boyle's Law and Charles' Law, relating pressure, volume, temperature, and the number of moles of gas. It is thus an equation of state.

It states, for a volume $V$ containing $n$ moles of a gas at pressure $P$ and temperature $P$, $$PV=nRT$$

where $R$ is the universal gas constant. For SI units, $$R=8.314 \frac{\text{J}}{\text{mol}\cdot\text{K}}$$

As a result, $\frac{PV}{T}=nR$ thus for any fixed number of moles of gas, the quantity $\frac{PV}{T}$ is constant.

This equation is relevant to low-density, low-pressure gases. For higher densities, it is necessary to correct this equation. For greater precision, the van der Waals equation is another equation of state which does apply to higher-pressure gases.

## Problems

### Introductory

If an ideal gas is in a container of dimensions 1 meter, 1 meter, and 2 meters, at a pressure of 100 kPa, and the container is reduced to 1/8th of its former dimensions while keeping the temperature constant, what will the pressure in the container be after reduction?