Pressure is the force gas molecules exert when they collide with the walls of their container, measured per unit of area. Temperature reflects the average kinetic energy, or motion, of the molecules within a substance. The direct answer is that pressure and temperature are directly proportional, meaning they rise and fall together, but this relationship only holds true under a very specific set of conditions.
The Core Principle: Pressure and Temperature in a Fixed Space
For the pressure and temperature of a gas to be directly proportional, two conditions must be strictly maintained: the amount of gas must remain constant, and the volume of the container must be fixed. When these two factors are unchanging, any increase in temperature will result in a proportional increase in pressure. This means that if you double the absolute temperature of the gas, the pressure inside the container will also double.
A common example is a sealed aerosol can left in a hot place. Since the can is rigid, its volume cannot change, and the amount of propellant gas inside is fixed. As the temperature increases, the pressure inside rises dramatically, creating a dangerous situation where the can may rupture. A similar effect is seen in car tires; pressure measurements are noticeably lower in the cold of winter than in the heat of summer.
This relationship is only mathematically proportional when temperature is measured on the absolute temperature scale, Kelvin. The Kelvin scale begins at absolute zero, the theoretical temperature at which all molecular motion stops. Measuring temperature in Kelvin ensures that a zero temperature corresponds to zero pressure, which is necessary for the direct proportional relationship to be accurate. If the Celsius or Fahrenheit scales were used, the relationship would still exist, but it would not be a simple proportionality.
The Underlying Mechanism
The physical reason behind the direct proportionality is explained by the Kinetic Molecular Theory (KMT), which describes the behavior of gas particles. The temperature of a gas is directly linked to the average kinetic energy of its constituent molecules. A higher temperature means the gas molecules are moving at a faster average speed.
When the temperature increases, these faster-moving molecules strike the inner walls of the container with greater force. Because the molecules are moving more quickly, they also increase the frequency of their collisions with the container walls. Pressure is defined by the cumulative force of these molecular collisions distributed over the container’s surface area.
Increasing the temperature thus translates to a dual effect: each molecular impact becomes harder, and the number of impacts occurring every second increases. Both factors contribute to the total outward force exerted on the container walls, which is perceived as an increase in pressure.
When the Relationship Changes
The direct proportionality between pressure and temperature is a specific case that depends entirely on the volume being held constant. In many real-world systems, such as a flexible balloon or a gas contained by a movable piston, the volume is not fixed and is allowed to change. When the volume is variable, the relationship between pressure and temperature becomes more complex.
If the temperature of a gas increases in a flexible container, the resulting increase in molecular kinetic energy causes the gas to push harder on the walls. Instead of the pressure rising indefinitely, the container expands, increasing the volume until the internal pressure is balanced by the external pressure. In this scenario, a temperature increase leads to a volume increase, not a pressure increase, assuming the external pressure remains the same.
The complexity further increases when the temperature is held constant and the volume is changed, which introduces an inverse relationship. If you decrease the volume of a gas while keeping its temperature steady, the pressure will increase because the molecules have less space to move and hit the walls more frequently.
To describe the behavior of a gas when none of the variables are held constant, a unified formula called the Ideal Gas Law is used. This law links pressure and temperature with volume and the amount of gas, showing how all four properties interact simultaneously. The initial simple, direct proportionality is just one specific condition—a fixed volume—of this larger, comprehensive relationship that governs gas behavior.