In gases, how does pressure relate to temperature at constant volume (Gay-Lussac's law)?

• A. Pressure is inversely proportional to temperature.
• B. Pressure is proportional to the square root of temperature.
• C. Pressure is proportional to temperature (P ∝ T) in Kelvin.
• D. Pressure remains constant regardless of temperature.

Answer: (C)

When the volume is fixed, increasing the temperature makes the gas molecules move faster and collide with the container walls more forcefully. Because temperature entered on the Kelvin (absolute) scale is directly linked to average kinetic energy, these faster collisions raise the pressure in direct, proportional fashion. So pressure scales linearly with temperature in Kelvin, meaning P ∝ T (in Kelvin). If the temperature doubles (in Kelvin) while the amount of gas and the volume stay the same, the pressure doubles as well. This linear relationship through the origin is why using Kelvin is essential for the proportionality.

The other patterns don’t match observed gas behavior at constant volume: pressure does not decrease with higher temperature, it doesn’t rise only with the square root of temperature, and it isn’t fixed as temperature changes.