Thermodynamics

334 | ThermodynamicsT∆S = S 2 – S 1 = 0.4 kJ/KIrreversibleprocess1Reversibleprocess0.3 0.7 S, kJ/KFIGURE 7–3The entropy change between twospecified states is the same whetherthe process is reversible orirreversible.2Entropy is an extensive property of a system and sometimes is referred to astotal entropy. Entropy per unit mass, designated s, is an intensive propertyand has the unit kJ/kg · K. The term entropy is generally used to refer toboth total entropy and entropy per unit mass since the context usually clarifieswhich one is meant.The entropy change of a system during a process can be determined byintegrating Eq. 7–4 between the initial and the final states:2¢S S 2 S 1 a dQ T b int rev1kJ>K21(7–5)Notice that we have actually defined the change in entropy instead ofentropy itself, just as we defined the change in energy instead of the energyitself when we developed the first-law relation. Absolute values of entropyare determined on the basis of the third law of thermodynamics, which isdiscussed later in this chapter. Engineers are usually concerned with thechanges in entropy. Therefore, the entropy of a substance can be assigned azero value at some arbitrarily selected reference state, and the entropy valuesat other states can be determined from Eq. 7–5 by choosing state 1 to bethe reference state (S 0) and state 2 to be the state at which entropy is tobe determined.To perform the integration in Eq. 7–5, one needs to know the relationbetween Q and T during a process. This relation is often not available, andthe integral in Eq. 7–5 can be performed for a few cases only. For themajority of cases we have to rely on tabulated data for entropy.Note that entropy is a property, and like all other properties, it has fixedvalues at fixed states. Therefore, the entropy change S between two specifiedstates is the same no matter what path, reversible or irreversible, is followedduring a process (Fig. 7–3).Also note that the integral of dQ/T gives us the value of entropy changeonly if the integration is carried out along an internally reversible pathbetween the two states. The integral of dQ/T along an irreversible path isnot a property, and in general, different values will be obtained when theintegration is carried out along different irreversible paths. Therefore, evenfor irreversible processes, the entropy change should be determined by carryingout this integration along some convenient imaginary internallyreversible path between the specified states.A Special Case: Internally ReversibleIsothermal Heat Transfer ProcessesRecall that isothermal heat transfer processes are internally reversible.Therefore, the entropy change of a system during an internally reversibleisothermal heat transfer process can be determined by performing the integrationin Eq. 7–5:which reduces to2¢S a dQ 2T b int rev a dQ b 1 T 0 int rev T 0 21111dQ2 int rev¢S Q T 01kJ>K2(7–6)