The Ideal Gas Law
Gas particles are constantly zooming around and bouncing off the walls of their container, and that is what creates pressure. Squeeze the gas into a smaller volume, heat it up, or add more gas particles, and the pressure rises, because the molecules crowd together or move faster and hit the walls harder and more often. The ideal gas law ties pressure, volume, amount of gas, and temperature together in one equation.
The formula
P · V = n · R · T
- P — pressure (Pa): the force per unit area the gas exerts on the walls of its container
- V — volume (m³): the amount of space the gas occupies
- n — amount of substance (mol): how many moles of gas particles are present
- R — gas constant (J/(mol·K)): a fixed number that connects the units of pressure, volume, amount, and temperature
- T — temperature (K): how hot the gas is, measured on the kelvin scale
Worked example
A container holds 1 mole of gas at a temperature of 300 kelvin, squeezed into a volume of 3 cubic meters. What pressure does the gas exert?
- n = 1 mol
- T = 300 K
- V = 3 m³
- P = n · R · T / V
- P = (1 mol · 8.31 J/(mol·K) · 300 K) / 3 m³
P = 831 Pa
Test yourself
If the temperature drops to 200 kelvin while the volume and amount of gas stay the same, what is the new pressure?
- Correct answer: 554 Pa
- 831 Pa
- 1662 Pa
Right! Lower temperature means lower pressure: one mole times eight point three one times two hundred, divided by three cubic meters, equals five hundred fifty-four pascals.
A balloon at constant pressure and amount of gas doubles in volume. What must happen to its temperature?
- It stays the same
- Correct answer: It doubles
- It is cut in half
Correct! At constant pressure, volume and temperature rise together, so doubling the volume doubles the temperature.
Where you see this
Car tires read higher pressure after a long summer drive — the rolling and flexing warm the air inside, and at fixed volume, warmer gas means more wall-hitting and more pressure. A sealed chip bag, meanwhile, puffs up like a pillow on a mountain drive: less outside air pressing inward lets the same trapped gas push the bag bigger.
Common mistakes
The most damaging slip is plugging Celsius into the equation — temperature here is absolute, in kelvin, and gas behavior depends on how fast molecules actually move, not on where water freezes. The second is treating P, V, n, and T as four independent knobs: with volume and amount fixed, cooling from 300 K to 200 K drops the pressure in exact proportion, P = n · R · T / V gives (1 mol × 8.31 × 200 K) ÷ 3 m³ = 554 Pa. Change one term and another must give.
How it connects
This is the founding equation of thermodynamics — it defines what temperature means for a gas (a reading of molecular motion) and how that motion becomes pressure. Calorimetry, next, asks what it costs in energy to change that temperature, and R is the same universal constant that reappears throughout thermodynamics.