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Specific Entropy

The entropy can be made into an intensive or specific, variable by dividing by the mass. Engineers use the specific entropy in thermodynamic analysis more than the entropy itself. The specific entropy (s) of a substance is its entropy per unit mass. It equals the total entropy (S) divided by the total mass (m).

s = S/m


s = specific entropy (J/kg)

S = entropy (J)

m = mass (kg)

T-s diagram of a thermodynamic cycle
T-s diagram of Rankine Cycle

Entropy quantifies the energy of a substance that is no longer available to perform useful work. Because entropy tells so much about the usefulness of an amount of heat transferred in performing work, the steam tables include values of specific entropy (s = S/m) as part of the information tabulated.

In general, specific entropy is a property of a substance, like pressure, temperature, and volume, but it cannot be measured directly. Normally, the entropy of a substance is given for some reference value. For example, the specific entropy of water or steam is given using the reference that the specific entropy of water is zero at 0.01°C and normal atmospheric pressure, where s = 0.00 kJ/kg. The absolute value of specific entropy is unknown is not a problem, however, because it is the change in specific entropy (∆s) and not the absolute value that is important in practical problems.

Temperature-entropy Diagrams – T-s Diagrams

The phases of a substance and the relationships between its properties are most commonly shown on property diagrams. A large number of different properties have been defined, and there are some dependencies between properties.

A Temperature-entropy diagram (T-s diagram) is the type of diagram most frequently used to analyze energy transfer system cycles. It is used in thermodynamics to visualize changes to temperature and specific entropy during a thermodynamic process or cycle.

The work done by or on the system and the heat added to or removed from the system can be visualized on the T-s diagram. By the definition of entropy, the heat transferred to or from a system equals the area under the T-s curve of the process.

dQ = TdS

An isentropic process is depicted as a vertical line on a T-s diagram, whereas an isothermal process is horizontal. In an idealized state, compression is a pump, compression in a compressor, and expansion in a turbine is isentropic processes. Therefore it is very useful in power engineering, because these devices are used in thermodynamic cycles of power plants.

Note that, the isentropic assumptions are only applicable with ideal cycles. Real thermodynamic cycles have inherent energy losses due to inefficiency of compressors and turbines.

Specific Entropy of Wet Steam

The specific entropy is included in the steam tables for pure substances like steam, similar to a specific volume, specific internal energy, and specific enthalpy.

The specific entropy of saturated liquid water (x=0) and dry steam (x=1) can be picked from steam tables. In case of wet steam, the actual entropy can be calculated with the vapor quality, x, and the specific entropies of saturated liquid water and dry steam:

swet = ss x + (1 – x ) sl              


swet = entropy of wet steam (J/kg K)

ss = entropy of “dry” steam (J/kg K)

sl = entropy of saturated liquid water (J/kg K)

Nuclear and Reactor Physics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2. 
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

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