Assumptions in the derivation of the kinetic theory of gases

In summary, the kinetic theory of gases involves dividing the change in momentum of a particle by the time over which the collision takes place, which is derived by dividing the total distance traveled by the particle in the box by its velocity. This assumption is based on the negligible size of the molecules compared to the size of the container.
  • #1
Miss_e101
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When deriving the kinetic theory of gases, we take the change in momentum of a particle as it hits one side of a box and divide it by the time over which the collision takes place. The time is derived by taking the total distance the particle traveled in the box (i.e. from one end, off the side and back again) divided by its velocity. However, why is it that we don't only take the time over which the collision with the wall occurred? Does this relate to the assumption that the size of the molecules is negligible compared with the size of the container?

Any assistance would be appreciated.

Cheers,
Miss_e101
 
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  • #2
The rate of change of momentum is the momentum transfer per collision times the number of collisions per second. The latter quantity is equal to 1/(time between collisions), which is 1/(distance between collisions/velocity), assuming the time taken by a collision is negligible.
 

1. What are the key assumptions in the derivation of the kinetic theory of gases?

The key assumptions in the derivation of the kinetic theory of gases include the assumption that gases are made up of a large number of particles that are in constant, random motion; that these particles have negligible volume compared to the volume of the gas; that the particles do not interact with each other except during collisions; and that the collisions between particles are elastic.

2. How do these assumptions impact the accuracy of the kinetic theory of gases?

These assumptions allow for the simplification of the behavior of gases and make the theory easier to apply. However, they also limit the accuracy of the theory as they do not account for real-world factors such as intermolecular forces and non-ideal behavior of gases at high pressures and low temperatures.

3. Are there any exceptions to these assumptions?

Yes, there are exceptions to these assumptions. For example, at high pressures and low temperatures, the volume of gas particles becomes significant and the assumption of negligible volume is no longer valid. Additionally, certain gases, such as polar gases, may exhibit non-ideal behavior due to intermolecular forces.

4. How does the kinetic theory of gases relate to other thermodynamic principles?

The kinetic theory of gases is closely related to the laws of thermodynamics, specifically the ideal gas law. The ideal gas law is derived from the kinetic theory of gases and describes the relationship between pressure, volume, temperature, and number of moles for an ideal gas.

5. Can the kinetic theory of gases be applied to all types of gases?

No, the kinetic theory of gases is most accurate for monatomic gases, such as helium and neon, and becomes less accurate for gases with more complex molecular structures. However, it can still provide useful approximations for these gases in certain conditions.

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