GATE PH 2022 PH Q47: Thermodynamics and Statistical Physics

A paramagnetic salt of mass

is held at temperature

in a magnetic field

. If

is the entropy of the salt and

is its magnetization, then

, where

is the Gibbs free energy. If the magnetic field is changed adiabatically by

and the corresponding infinitesimal changes in entropy and temperature are

and

, then which of the following statements are correct

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