JANUARY, 1953
39
A NOTE ON THE ENTROPY OF A SYSTEM UNDERGOING IRREVERSIBLE PROCESSES MILTON KERKER Clarlraon College of Technology, Potsdam, New York
A NUMBER of textbooks of chemical thermodynamics ' - 8 treat the entropy change experienced by an isolated system undergoing irreversible processes. The purpose of such treatments is to show that
so that
+
DQ DQ dSsy8tsm= dSmedimm dSsuw. > T -T >0
(5)
Equation (4) requires that the surroundings themThis point is often a source of confusion to many students who feel that it The first step is to state that for any process implies that the surroundings must necessarily change dS B DQ (2) reversibly in order that the proof be successful. They feel that the medium and surroundings are inseparably where the equality pertains to a reversible process and involved in the same process and the restriction of the the inequality to an irreversible process. This state- surroundings to reversible changes sti-ikes them as being ment can be derived from one of the enunciations of t,he artificial. It isunnecessary to make this restriction and Second Law or it may be stated axiomatically as the the treatment is actually more general and natural if the Second Law. surroundings are also permitted to change irreversibly. The isolated system is then divided into a medium In such a case and surroundings. Each infinitesimal step of the process is characterized by a transfer of heat from the surroundings to the medium which undergoes an irreversible process. Let the heat absorbed by the medium be DQ and that absorbed by the surroundings be -DQ. The usual formulation states that and dSs7stem> 0
(1) selves undergo a reversible process.
If there is a temperature difference between the system and surroundings,
TI:.]
1 K ~ o n I. , M., "Chemical Thermodynamics," Prentice-Hall, DQ DQ Tsar.Inc., New York, 1950, pp. 96-7. d s . ~ - > ~madiv~ = DQ[~..,. a G ~ ~SAMUEL, s ~ "Thermodynamics ~ ~ ~ ~ ,for Chemists," D. Van Nostrand Ca., Inc., New York, 1947, pp. 144-6. a STEINER, LR.,"Introduction to Chemical ~ h ~ ~ ~ d ~ since . ~ DQ i ~> ~0 when , " Teurn > Trnediurnr and DQ Taurr.< Trnadium 2nd ed., MeGraw-Hill Book Co., Inc., New York, 1948, p. 164.
>0
(6)
< 0 when
