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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
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National Cancer Institute, Bethesda, (2011).
[4] R.L. Siegel, K.D. Miller, A. Jemal, Cancer statistics, 2019, CA Cancer J. Clin. 69 (1)
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[5] L. Ries, M.P. Eisner, C.L. Kosary, et al. SEER Cancer Statistics Review, 1975–2002, Na-
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