Entropy change in an inelastic collision.

[bbhill]

1. A 3 kg mass hits a stationary mass of 9 kg and sticks. What is the change in entropy?



So, I figure that I will need to $$\Delta$$S = $$\Delta$$Q$$/$$T.

However, I don't know the heat or the temperature of this reaction, so this couldn't possibly be the way to evaluate.

So, I think I could use S = k ln (number of microstates) and find the difference between the initial and final values of S. However, how would I calculate the number of microstates for this system?

 

[kuruman]

Inelastic collisions do not conserve kinetic energy. Here, the kinetic energy after the collision is less than before. However, total energy is always conserved. So, to what kind of energy is the lost kinetic energy transformed?

 

[tomcue]

I would first clarify that the concept of entropy change in an inelastic collision is not well-defined. Entropy is a measure of the disorder or randomness of a system, and in an inelastic collision, the total energy of the system is not conserved. Therefore, the concept of entropy, which is closely related to energy, cannot be accurately calculated in this scenario.

However, if we were to consider the change in entropy of the individual masses before and after the collision, we could use the formula \DeltaS = \int \frac{\delta Q}{T} to calculate the change in entropy for each mass. Here, \delta Q represents the heat transferred during the collision, and T is the temperature of the system.

In order to calculate \delta Q, we would need to know the specific heat capacity of the masses and the temperature change during the collision. This information can be used to determine the change in entropy for each mass, and the overall change in entropy can be calculated by summing up these individual changes.

Alternatively, we could also use the formula S = k ln (number of microstates) to calculate the change in entropy for each mass, as mentioned in the original content. However, as the number of microstates is difficult to determine for this system, this approach may not provide an accurate value for the change in entropy.

In conclusion, while it is possible to calculate the change in entropy for each individual mass in an inelastic collision, the concept of overall entropy change for the system is not applicable in this scenario.