What are the assumptions of the kinetic theory of gases, and does it still account for conservation of energy? Shouldn't the system energy decrease eventually?
2 Answers
When the gaseous molecules collide, the collisions are 'elastic' meaning that the combined energy of both colliding molecules is the same both before and after a collision.
Explanation:
The Kinetic theory of gases assumes that all molecules of gas in a system are very small compared to the distances between them all and that they are all continually moving in random motions. When they each collide, the collisions are described as 'elastic' meaning that combined energy of the gases colliding doesn't change after the collision, even if the individual gases themselves change energy. The energy transfer is perfect between the colliding particles.
This means that the energy within the system therefore is held constant as the TOTAL energy in the system is the same as long as the system remains unchanged.
If you imagine a single room with four people in and each person goes into the room with two balls each, when the door on the room is closed (i.e. a system). There are four people and eight balls in the system, even if the people exchange balls and one person ends up with three balls and one person with one ball, there will still only be eight balls in the room at any one time. If you imagine the people are molecules of gas and the balls are units of energy, hopefully it might make a little sense!
The kinetic theory of gases states that the total energy for all molecules in a system is conserved, meaning that the total energy is not expected to change over time GIVEN the assumptions made.
...And the assumptions are:
- The collisions made are elastic, transferring kinetic energy completely.
- The gas particles are non-interacting masses of negligible volume relative to their container.
- The ensemble of gas particles produces a distribution of speeds, so that the average kinetic energy of the ensemble of gases is proportional to the temperature of the sample.
This claims that since the collisions are elastic, energy is conserved over a time in which the system is in a steady state. This means that as long as the energy lost is small, there is no noticeable change in total energy.
After infinite time, yes, the energy of the system will have decreased, but that energy would transfer over to a different system nearby.
In the end, energy is still conserved within the universe.
