Answer to Question #73670 in Quantum Mechanics for rohan yadav

Question

What is gibbs paradox?why it does arises?

Answer 1

In statistical mechanics, a semi-classical derivation of the entropy that does not take into account the indistinguishability of particles, yields an expression for the entropy which is not extensive (is not proportional to the amount of substance in question). This leads to a paradox known as the Gibbs paradox, after Josiah Willard Gibbs. The paradox allows for the entropy of closed systems to decrease, violating the second law of thermodynamics.
Gibbs paradox arises not due to application of thermodynamic considerations - whether classical or statistical or even quantum mechanical – but due to incorrect application of mathematics to the process of mixing of ideal gases. The paradox is not connected with the nature of properties of extensivity and additivity of entropy.