ENTROPY
Any reversible path may be substituted by a reversible zigzag path between the same end states, consisting of a reversible adiabatic followed by a reversible isotherm and then by reversible adiabatic such that the heat transferred during the isothermal process is the same as that transfered during the original process.
The entropy of a system is a thermodynamic property which is a measure of the degree of molecular disorder existing in the system. It describes the randomness or uncertainity of the system, It ios a function of a quantity of heat which shows the possibility of conversion of heat into work. Thus, for maximum entropy, there is minimum availability for conversion into work and for minimum entropy there is a maximum availability for conversion into work.
Characteristics:
=> dS = 0 (∵ dQ = 0)
∴ S = constant
Thus a reversible adiabatic process is an isentropic process.
At a temperature, T_{o}
CLAUSIS' INEQUALITY
The Clausius theorem (1855) states that a system (heat engine or heat pump) exchanging heat with external reservoirs and undergoing a cyclic process, is one that ultimately returns a system to its original state,
wheretemperature of the external reservoir (surroundings) at a particular instant in time.
is the infinitesimal amount of heat absorbed by the system from the reservoir and is theRemember:
Equality sign holds good for a reversible process and the inequality sign for an irreversible process.
• Entropy principle:
For an isolated reversible system
For an isolated irreversible system
The total entropy of an isolated system can never decrease over time, and is constant if and only if all processes are reversible. Isolated systems spontaneously evolve towards thermodynamic equilibrium, the state with maximum entropy.
• It is also a statement of second law of thermodynamics.
• Entropy increase of the isolated system is a measure of the extent of irreversibility
of the process under gone by the system.
• When the system is at equilibrium, any conceivable change in entropy would be
zero.
Application of entropy principle
• Transfer of heat through a finite Temperature difference.
Mixing of two fluids
Final temp (t_{f}) =
Maximum work obtainable from two finite identical bodies at T_{1} and T_{2}.
Final temperature of the two bodies (T_{f}) =
with maximum delivery of work.
T = temp. of body
To = temp. of TER
Equation  Holds good for 
dQ = dE+ dW  Reversible, Irreversible, any system 
dQ = dU + dW  Reversible, Irreversible, Closed System. 
dQ = dU + pdV  Reversible, Closed system 
dQ = TdS  Reversible 
TdS = dU + PdV  Reversible, Irreversible, Closed system 
TdS = dH – Vdp  Reversible, Irreversible, Closed system 
c : specific heat for solid, liquid
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