Gibbs paradox
Imagine you have a box full of marbles that are either red or blue. You want to know the probability of picking a red marble if you blindly reach into the box. To do this, you count how many red marbles are in the box and divide by the total number of marbles. Easy peasy, right?
Now imagine you have two boxes, each with the same number of marbles, but one box is all red marbles and the other is all blue marbles. You want to know the probability of picking a red marble from the combined boxes.
Here's where things get interesting - do you still count only the red marbles and divide by the total number of marbles? Or do you count both the red and blue and divide by the total number?
This question is at the heart of Gibbs paradox, named after physicist J. Willard Gibbs. Gibbs realized that if you counted only the red marbles, you'd get a different probability than if you counted both the red and blue marbles.
In thermodynamics, the paradox arises in the calculation of the entropy of a system composed of many identical particles. Entropy is a measure of disorder or randomness, and it's used to describe the energy in a system that cannot be harnessed to do useful work.
When you have a large number of identical particles, the entropy calculation becomes tricky. Gibbs discovered that in some cases, counting only the particles of interest (like counting only the red marbles) gave a different result than counting all the particles (like counting both red and blue marbles).
This paradox caused much confusion and debate among physicists, but ultimately led to a deeper understanding of statistical mechanics and the nature of entropy. So, in short, the Gibbs paradox is a tricky situation where counting only part of a system may lead to a different result than counting the whole system.
Now imagine you have two boxes, each with the same number of marbles, but one box is all red marbles and the other is all blue marbles. You want to know the probability of picking a red marble from the combined boxes.
Here's where things get interesting - do you still count only the red marbles and divide by the total number of marbles? Or do you count both the red and blue and divide by the total number?
This question is at the heart of Gibbs paradox, named after physicist J. Willard Gibbs. Gibbs realized that if you counted only the red marbles, you'd get a different probability than if you counted both the red and blue marbles.
In thermodynamics, the paradox arises in the calculation of the entropy of a system composed of many identical particles. Entropy is a measure of disorder or randomness, and it's used to describe the energy in a system that cannot be harnessed to do useful work.
When you have a large number of identical particles, the entropy calculation becomes tricky. Gibbs discovered that in some cases, counting only the particles of interest (like counting only the red marbles) gave a different result than counting all the particles (like counting both red and blue marbles).
This paradox caused much confusion and debate among physicists, but ultimately led to a deeper understanding of statistical mechanics and the nature of entropy. So, in short, the Gibbs paradox is a tricky situation where counting only part of a system may lead to a different result than counting the whole system.