P M V Subbarao Professor Mechanical Engineering Department The Entropy Change P M V Subbarao Professor Mechanical Engineering Department A Single Reason for Every Thing That Happens!!!

Carnot Gas Engine : The Reversible Cycle

Carnot Engine using Phase Change Substance : SSSF CVs HTR Boiler 2 1 Turbine Compressor 4 3 Condenser LTR

Performance of Reversible Cycle Use a generalized indices…

During a time duration  For a reversible cycle with n number heat transfer processes Where, i shows ith process and n is the number of process in a cycle. But Qi is a path function and depends on process.

Therefore, k is an initial state and k+1 is a final state. m is the number state Points in a cycle. Therefore for all reversible cycles.

A New cyclic Integral Cyclic integral of this new quantity is zero! Any quantity whose cyclic integral is zero is a property ! For a reversible process an infinitesimal change in this new property is: Boltzman named S as Entropy of a substance. During a reversible process

Entropy, S : A Measure of State of Matter So (J/K•mol) H2O(liq) 69.95 H2O(gas) 188.8 For a given substance S (gaseous state) > S (liquid state) > S (solid state)

Entropy and Order of Molecules of Matter S˚(Br2 liq) < S˚(Br2 gas) S˚(H2O solid) < S˚(H2O liquid)

Entropy, S : Molecular Complexity Increase in molecular complexity generally leads to increase in S.

Standard Molar Entropies

Entropy and Temperature S increases slightly with T S increases a large amount with phase changes

Entropy Change during a Reversible Process From the definition of the entropy, it is known that Q=TdS during a reversible process. The total heat transfer during this process is given by Qreversible =  TdS Therefore, it is useful to consider the T-S diagram for a reversible process involving heat transfer On a T-S diagram, the area under the process curve represents the heat transfer for a reversible process T S A reversible adiabatic process

Flow Boiling Process T h Liquid Liquid +Vapour Vapour Vapour

Steam Generation : Expenditure Vs Wastage Vapour Liquid +Vapour h Liquid s

Analysis of Steam Generation at Various Pressures Specific Pressure Enthalpy Entropy Temp Volume MPa kJ/kg kJ/kg/K C m3/kg 1 3500 7.79 509.9 0.3588 2 5 7.06 528.4 0.07149 3 10 6.755 549.6 0.03562 4 15 6.582 569 0.02369 20 6.461 586.7 0.01776 6 25 6.37 602.9 0.01422 7 30 6.297 617.7 0.01187 8 35 6.235 631.3 0.0102

Variable Pressure Steam Gneration h s

Carnot Cycle Show the Carnot cycle on a T-S diagram and identify the heat transfer at both the high and low temperatures, and the work output from the cycle. S T TH TL S1=S4 S2=S3 1 2 3 4 A B 1-2, reversible isothermal heat transfer QH = TdS = TH(S2-S1) area 1-2-B-A 2-3, reversible, adiabatic expansion isentropic process, S=constant (S2=S3) 3-4, reversible isothermal heat transfer QL = TdS = TL(S4-S3), area 3-4-A-B 4-1, reversible, adiabatic compression isentropic process, S1=S4 Net work Wnet = QH - QL, the area enclosed by 1-2-3-4, the shaded area

Nature of Reversible Machines For all reversible heat engines: For all reversible heat pumps and refrigerators: Therefore all reversible machines in this universe :

Process : h-s Diagram : Mollier Diagram Enthalpy-entropy diagram, h-s diagram: it is valuable in analyzing steady-flow devices such as turbines, compressors, etc. Dh: change of enthalpy from energy balance (from the first law of thermodynamics) Ds: change of entropy from the second law. A measure of the irreversibilities during an adiabatic process. Ds Dh h s

Enthalpy Vs Entropy Diagram