Gas Laws and Pressure

What is gas pressure?

The kinetic theory of gases pictures a gas as tiny particles moving quickly in straight lines, bouncing off each other and the walls. Every time a particle bounces off a wall, it gives the wall a small push.Pressure is the total force of all those pushes on each square metre of wall:

Pressure rises if the particles hit the walls more often or harder. Every gas law comes from those two ideas. Normal air pressure at sea level is about 101 kPa.

Temperature in kelvin

Temperature measures the average kinetic energy of the particles, and the gas laws only work if it is measured fromabsolute zero, the temperature at which particle motion would be at its minimum. The kelvin scale does this: 0 K = −273.15 °C, and a change of 1 K equals a change of 1 °C.

Boyle’s law

At constant temperature and amount of gas, pressure is inversely proportional to volume. Halve the volume and the particles have half as far to travel between collisions, so each part of the wall is hit twice as often: the pressure doubles. A pressure–volume graph is a curve, and P × V stays the same.

Charles’s law

At constant pressure and amount of gas, volume is proportional to the kelvin temperature. Heating makes the particles faster, so they push harder on a free piston; it rises until the pressure inside again matches the pressure outside. Plotted against kelvin temperature, the volume is a straight line through the origin.

The pressure–temperature law

At constant volume and amount of gas, pressure is proportional to the kelvin temperature. This is often called Gay-Lussac’s law (or Amontons’s law). In a rigid container, faster particles hit the walls both more often and harder. Extending the straight line on the graph backwards to zero pressure points to absolute zero, which is how scientists first estimated it.

The ideal gas law

Adding more gas also raises the pressure (or the volume): more particles mean more collisions. This isAvogadro’s law: at the same temperature and pressure, equal volumes of gas contain equal numbers of particles. All four relationships combine into one equation:

P is pressure in pascals, V is volume in m³, n is the amount in moles, T is temperature in kelvin and R is the gas constant, 8.314 J/(mol·K). For example, 0.20 mol at 300 K in 2.5 L gives P = 0.20 × 8.314 × 300 ÷ 0.0025 ≈ 200 kPa, which is the simulator’s starting state.

Key terms and formulas

Pressure (P)

Force per unit area, measured in pascals (Pa) or kilopascals (kPa).

Absolute zero

0 K, −273.15 °C: the lowest possible temperature.

Ideal gas

A model gas whose particles take up no space and do not attract each other. Real gases behave almost ideally at ordinary temperatures and pressures.

Combined gas law

P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂ for a fixed amount of gas.

Real-world applications

• Breathing: your diaphragm enlarges your chest, lowering the air pressure in your lungs so that air flows in (Boyle’s law).
• Hot-air balloons: heated air expands, so the air inside is less dense than the cooler air outside (Charles’s law).
• Tyres are checked when cold, because driving warms them and raises their pressure.
• Aerosol cans carry warnings not to heat them: in a rigid can the pressure rises with temperature.
• Divers must breathe out while rising, because the air in their lungs expands as the water pressure falls.

Common misconceptions

• “Heated gas particles get bigger.” They move faster; the gas takes up more space only because they push the walls further apart.
• “Doubling the Celsius temperature doubles the pressure.” Only kelvin temperatures are proportional.
• “Pressure comes from the gas’s weight.” It comes from collisions, and pushes equally in every direction.
• “Gas particles stop at 0 °C.” At 0 °C (273 K), air molecules average about 450 m/s.

What the model simplifies

The simulator is two-dimensional and uses an ideal gas: each dot represents about 6 × 10²⁰ molecules (0.001 mol), the dots take up no space, do not attract each other and, as in the simplest kinetic theory, bounce only off the walls and not off each other. The bottom and side walls exchange heat with the gas; the piston is insulated. The gauge really is measured from the simulated collisions, averaged over three seconds, and then converted to kilopascals with a fixed calibration factor so that it can be compared with PV = nRT. Because there are only a few hundred dots, measured values fluctuate by a few percent, just as real measurements have random error. The molecular speed readout is the real average speed of nitrogen molecules at the gas temperature; the dots on screen move far more slowly so that you can follow them. Real gases deviate from PV = nRT at high pressures, when the particles’ own size matters, and at low temperatures, when their attractions matter and they eventually condense.

Key takeaways

• Gas pressure is caused by particles colliding with the walls of their container.
• Boyle’s law: at constant T and n, P × V is constant.
• Charles’s law: at constant P and n, V ÷ T is constant (T in kelvin).
• Pressure–temperature law: at constant V and n, P ÷ T is constant (T in kelvin).
• All of them combine into the ideal gas law, PV = nRT.