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References      19




                  less than the heat supplied into the system. For closed system, the second law of
                  thermodynamics is expressed as:

                                                  2 δ Q 
                                                   
                                           S − S =     +  S gen                 (1.40)
                                               1 ∫ 
                                           2
                                                  1   T   b                                                                                S −S =∫12δQTb+Sgen
                                                                                                                                              2
                                                                                                                                                 1

                     In Eq. (1.40) “b” is the system boundary, T is absolute temperature, Q is the rate                                     Q˙
                  of energy transfer by heat, and S  is the amount of entropy generated by system
                                             gen
                  irreversibility. The irreversibility associated with a process (I) may be expressed by:
                                                I  = T S gen                     (1.41)                                                      I=T Sgen
                                                    0
                                                                                                                                               0
                     The destruction of exergy due to irreversibility within the system is I and T  is
                                                                                  0
                  temperature of the surroundings. The second law of thermodynamics for steady-flow
                  system may be expressed as:
                                      dS cv  = ∑ Q   j  +  ∑ ms  −  ∑ ms  + S    (1.42)


                                      dt   j  T j  i  ii  e  ee  gen                                                                      dScvdt=∑jQ˙jTj+∑im˙isi−∑em˙ese
                                                                                                                                                     +Sgen
                     Entropy in the microscopic or statistical view is a logarithm measure of the num-
                  ber of states (X ) with significant probability of being occupied as is given as:
                              i
                                                =
                                               S σ B  ln  X i                    (1.43)                                                     S=σBlnXi
                                                                −1
                                                            −2
                                                        2
                  σ  is the Boltzmann constant (= 1.38 × 10 −23  m  kg s  K ) [53].
                   B
                  1.8.3.4  The third law of thermodynamics
                  The third law of thermodynamics is formulated by Walter Nernst, also known as the
                  Nernst heat theorem, and is based on the studies of chemical reactions at low tem-
                  peratures and specific heat measurements at temperatures approaching absolute zero.
                  The third law of thermodynamics states that the entropy of substances is zero at the
                  absolute zero of temperature. An example is pure crystalline substance that has zero
                  entropy at the absolute zero of temperature, 0 K.

                  References
                  [1] R. Siegel, D. Naishadham, A. Jemal, Cancer statistics, CA Cancer J. Clin. 62 (1) (2012)
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                  [2] L.S. Ries, M.A. Smith, J.G. Gurney, Cancer Incidence and Survival Among Children and
                     Adolescents: United States SEER Program 1975–1995, National Cancer Institute, Bethes-
                     da, (1999) Publ No 99-4649.
                  [3] N. Howlader, A.M. Noone, M. Krapcho, et al. SEER Cancer Statistics Review, 1975–2008,
                     National Cancer Institute, Bethesda, (2011).
                  [4] R.L. Siegel, K.D. Miller, A. Jemal, Cancer statistics, 2019, CA Cancer J. Clin. 69 (1)
                     (2019) 7–34.
                  [5] L. Ries, M.P. Eisner, C.L. Kosary, et al. SEER Cancer Statistics Review, 1975–2002, Na-
                     tional Cancer Institute, Bethesda, (2005) based on November 2004 SEER data submission
                     http://seer.cancer.gov/csr/1975_2002/.
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