Answer to Question #89773 in Molecular Physics | Thermodynamics for Shivam Nishad

Question

What is Gibb's paradox ? Why does it arise ?
Obtain Sackur-Tetrode equation and show that it is free from Gibb's paradox.

Answer 1

In Thermodynamics, the Gibbs paradox is about entropy of mixing gases. It says thatthe entropy of mixing decreases discontinuously with similarity andreaches zero for identical gases at same pressure and temperature. It becomes paradox if one assumes that eachparticle is distinguishable irrespective of nature of gases mixed togetherand applies equation of state of an ideal gas.

In quantum mechanics, which is what we really should be using to study microscopic phenomena, the essential indistinguishability of atoms and molecules is hard-wired into the theory at a very low level. A paradox arises if we try to treat molecules as if they were distinguishable. This is called Gibb's paradox.

The resolution of Gibb's paradox is quite simple: treat all molecules of the same species as if they were indistinguishable.

The Sackur–Tetrode equation is an expression for the entropy of a monatomic classical ideal gas which incorporates quantum considerations which give a more detailed description of its regime of validity