why temperature increases randomness increase then entrophy increases then ds=q*t?2. why in reversible process ds(total)=0 and in the irrreversible process ds(total)>0?3. why we are takingdG=(-ve) for spontaneous process explain

Dear student,

Entropy was first defined and used in 1865, long before the behavior of molecules was understood. Chemists and physicists had no idea that temperature was due to the motional energy of molecules or that “heat” was actually the transferring of that motional molecular energy from one place to another. Back then, entropy change, ΔS, could only be described in macro terms that could be measured, such as volume or temperature or pressure. The 1865 equation that is still completely correct is stated in most modern texts as simply ΔS = q (rev)/T.