One kilogram of water at room temperature is brought into contact with a high temperature thermal reservoir. The entropy change of the universe is

If a closed system is undergoing an irreversible process, the entropy of the system

$$2$$ moles of oxygen are mixed adiabatically with another $$2$$ moles of oxygen in mixing chamber, so that the final total pressure and temperature of the mixture become same as those of the individual constituents at, their initial states. The universal gas constant is given as $$R$$. The change in entropy due to mixing, per mole of oxygen, is given by

Which of the following relationships is valid only for reversible process undergone by a closed system of simple compressible substance (neglect changes in kinetic and potential energy?