Final answer:
The pressure exerted by a gas in a sealed, rigid container that is heated from 200 K to 400 K increases by a factor of 2, following Gay-Lussac's law, which states that pressure is directly proportional to temperature in Kelvin.
option d is the correct
Step-by-step explanation:
When a sample of a gas is heated in a sealed, rigid container from 200 K to 400 K, the pressure exerted by the gas is increased by a factor of 2. This is because the gas follows Gay-Lussac's law, which states that the pressure of a gas is directly proportional to its temperature when the volume and the number of gas molecules remain constant. Doubling the temperature from 200 K to 400 K will therefore double the pressure in a sealed, rigid container. Here's a brief explanation of the concept:
- The initial state of the gas is at 200 K, and it is subjected to a certain pressure.
- When the temperature is increased to 400 K, the kinetic energy of the gas molecules increases.
- As the kinetic energy increases, the collisions against the container walls become more frequent and forceful.
- Since the container is rigid, the volume does not change, nor does the number of gas molecules.
- Thus, under these conditions, according to Gay-Lussac's law, the pressure is directly proportional to the temperature expressed in Kelvins.
- Hence, when the temperature doubles, the pressure exerted by the gas also doubles.
The pressure increase is not a factor of 200, as that would imply a much more dramatic change than what would occur due to the direct proportionality between temperature and pressure.