Using the new cylinder the heat rate between the reservoirs would be 50 W
Conduction could be described by the Law of Fourierin the form: where is the rate of heat transferred by conduction, is the thermal conductivity of the material, and are the temperatures of each heat deposit, is the cross area to the flow of heat, and is the distance that the flow of heat has to go.
For the original cylinder the Fourier's law would be: , and if , then the expression would be: where is the diameter of the original cylinder, and is the length of the original cylinder.
For the new cylinder, in the same fashion that for the first, Fourier's Law would be: ,where is the heat rate in the second case, and are the new diameter and length.
But, and , substituting in the expression for : .
In the last declaration of , it could be noted that the expressión inside the parenthesis is actually , then: .
<u>It should be noted, that the temperatures in the hot and cold reservoirs never change.</u>
The moment of inertia of the system decreases and the angular speed increases.
This very concept might not seem to be interesting at first, but in combination with the law of the conservation of angular momentum, it can be used to describe many fascinating physical phenomena and predict motion in a wide range of situations.
In other words, the moment of inertia for an object describes its resistance to angular acceleration, accounting for the distribution of mass around its axis of rotation.
Therefore, in the course of this action, it is said that the moment of inertia of the system decreases and the angular speed increases.