Entropy has great importance in thermodynamics. It is a state function and it is a measure of the degree of disorder or randomness of the system. More is the disorder of the system, greater will be the entropy and vice versa. It is normally expressed in terms of change of entropy. (i) For a reaction entropy change is given by DeltaS=sumS("product")-sumS("reactant") (ii) DeltaS=(Q_(rev))/(T)=(W_(rev))/(T)=(nRT ln (V_(2)//V_(1)))/(T) =nRT ln (V_(2))/(V_(1))=nR ln (P_(1))/(P_(2)) (iii) DeltaS=DeltaH-TDeltaS (iv) Entropy change in reversible and irreversible process : Consider a Carnot cycle as shown in figure below in which ab and cd are isothermal. Irrespective of the path of the system in its reversible change, dq//T is same For entire Carnot cycle (dq_(1))/(T_(1))-(dq_(2))/(T_(2))=0 :. DeltaS_("universe")=DeltsS_("system")+DeltaS_("surrounding") DeltaS_("Surrounding")=(q_(1))/(T_(1))+(q_(2))/(T_(2)) (q term includes their own sign) bc and da are adiabatics. Let dq_(1) be the heat supplied to the working system at T_(1) K and dq_(2) be heat rejected by it to the sink at T_(2) K. All these steps are reversible. In a Carnot cycle. (dq_(1)-dq_(2))/(dq_(1))=(T_(1)-T_(2))/(T_(1)) or (dq_(1))/(T_(1))=(dq_(2))/(T_(2)) Let us now confine our attention only to the change of the system from point 'a' to point 'c' and attempt to find out the ratio of heat change to the temperature at which thermal changes occur by proceeding from a to c either along abc or adc. Along the path abc, ("Heat change")/("Temp.")=(dq_(1))/(T_(1)) Along the path adc, ("Heat change")/("Temp")=(dq_(2))/(T_(2)) In case of spontaneous and irreversible expansion to volume V_(1)+V_(2), W=0 and so will be DeltaU In the reversible expansion of the gas at T K from volume V_(1) to V_(1)+V_(2), heat absorbed DeltaU+RT ln (V_(1)+V_(2))/(V_(1)) (v) Suppose n moles of an ideal gas are enclosed in a vessel A of volume V_(1) which is connected through a stop cock to a completely evacuated vessel B of volume V_(2). The system is insulated and has temperature T K. If the stop cock is opened, the gas will attain the volume V_(1)+V_(2). In a reversible isothermal expansion of the gas at T K as shown in figure II, the DeltaS_("system"), DeltaS_("surroundings") and DeltaS_("universe") will be respectively ?