Explain why increasing the temperature of a gas in a closed, rigid container causes the pressure in the container to increase.
Gas expands when it is heated.
When you increase the temperature of a gas in a closed, rigid container, the pressure in the container increases due to a phenomenon known as the Ideal Gas Law. The Ideal Gas Law states that the pressure (P) of a gas is directly proportional to its temperature (T), when the volume (V) and the number of gas molecules (n) are constant. Mathematically, this can be expressed as:
P ∝ T
To understand why increasing temperature leads to an increase in pressure, let me explain the underlying mechanisms:
1. Molecular Motion: When you raise the temperature of the gas, the kinetic energy of the gas molecules increases. This increase in kinetic energy translates into higher molecular motion, causing the gas molecules to move more rapidly and collide with each other and the walls of the container more frequently and with greater force.
2. Increased Frequency of Collisions: The higher molecular motion leads to an increase in the frequency of collisions between gas molecules and the container walls. As a result, the container walls experience more frequent and forceful impacts from the gas molecules, exerting a higher pressure.
3. More Energetic Collisions: Along with increased frequency, the collisions become more energetic as the gas molecules possess higher kinetic energy. The higher energy collisions impart more force on the container walls with each collision, contributing to an increase in overall pressure.
So, when you heat the gas inside a closed, rigid container, the gas molecules move faster, collide with each other and the container walls more frequently, and exert a higher force on the walls. This increased force per unit area leads to an increase in pressure within the container.
In summary, increasing the temperature of a gas in a closed, rigid container causes the pressure to rise due to the enhanced molecular motion and more frequent, energetic collisions of the gas molecules with each other and the container walls.