Pressure and the gas laws.

Step 1 of 6

What pressure is

The Scene shows a sealed glass box with a wall you can move, holding 200 particles of nitrogen at 300 K. Each particle stands for an enormous number of real molecules, so the box behaves like 2 L of air: the gauge on the fixed end shows a pressure of one atmosphere, about 101 kPa.

Pressure is force per unit area, $p = \dfrac{F}{A}$⁠, and its unit is the pascal: a newton per square metre. Watch the particles hitting the walls.

Step 2 of 6

Squeeze

When the volume shrinks, each particle crosses the box sooner and reaches the wall more often. The same particles, at the same speed, hit more: the pressure rises.

Temperature and Amount of gas are now fixed. Guess what the gauge will show when you push Volume from 2 L to 1 L.

Step 3 of 6

Boyle’s law

At constant temperature and a fixed amount of gas, pressure and volume are inversely related: when one grows some number of times, the other shrinks by the same number. Their product does not change:

$p_1 V_1 = p_2 V_2$⁠

That is Boyle’s law. Now the wall is at 1.6 L: work out the pressure yourself first, and only then look at the gauge.

Step 4 of 6

Heat it

When a gas is heated, its particles move faster: each hit is harder, and the hits come more often. At constant volume the pressure rises, in proportion to the absolute temperature:

$\frac{p_1}{T_1} = \frac{p_2}{T_2}$$\frac{p_1}{T_1} =$$\frac{p_2}{T_2}$⁠

That is Gay-Lussac’s law. If the gas is heated at constant pressure instead, it expands in the same ratio, $\dfrac{V_1}{T_1} = \dfrac{V_2}{T_2}$$\dfrac{V_1}{T_1} =$$\dfrac{V_2}{T_2}$⁠: Charles’s law. Volume and Amount of gas are now fixed, and Temperature is free.

Step 5 of 6

Why kelvin

These ratios only work in kelvin. A gas at 0 °C still has a pressure, so you cannot divide by degrees Celsius: warming from 10 °C to 20 °C doubles nothing. The zero of the kelvin scale is where the pressure of an ideal gas would reach zero.

Step 6 of 6

More gas

The third way to raise the pressure is to add particles: each extra particle adds hits. Temperature and Volume are now fixed, and Amount of gas is free. Together the three laws make one equation, the ideal gas equation:

$pV = nRT$⁠

where $n$⁠ is the number of moles and $R = 8.314\ \mathrm{J/(mol \cdot K)}$$R =$$8.314\ \mathrm{J/(mol \cdot K)}$⁠ is the gas constant.