CHAPTER 19 SECTION 2 ENTROPY AND THE SECOND LAW OF THERMODYNAMICS

Recall that spontaneous processes (in reality) are irreversible. Original conditions can never be re-established perfectly. This fact can allow us to make predictions about the spontaneity of a process. The thermodynamic quantity called entropy is associated with the extent of randomness or disorder in a system or with the extent to which energy is distributed or dispersed among the various motions of the molecules of the system. Changes in entropy can be related to heat transfer and temperature.

ENTROPY CHANGE The change in entropy (ΔS) in a system depends only on the initial and final states of the system: ΔS = S final - S initial If the process has no temperature change (isothermal), ΔS is equal to the heat that would be transferred if the process were reversible (q rev ) divided by the temperature at which the process occurs: ΔS = q rev /T (T is constant)

ΔS FOR A PHASE CHANGE The melting or boiling of a substance is an isothermal process (no ΔT). In the example of the melting of ice, q = ΔH fusion and T = 0 0 C = 273 K The transfer of heat (q) is from the surroundings into the ice and the enthalpy of fusion for solid water (Δh fus ) = 334 J/g or 6.01 kJ/mol The melting is an endothermic process, and so the sign of ΔH is positive.

To calculate ΔS fusion for melting one mole of ice at 273 K: ΔS fus = q rev /T = ΔH fus /T = (1 mole)(6.01 x 10 3 J/mol) 273 K = 22.0 J/K So, this is the measure of the change in entropy when one mole of ice melts to liquid, a positive increase in disorder (solid  liquid)

THE SECOND LAW OF THERMODYNAMICS Unlike energy which is conserved in any process, entropy actually increases in any spontaneous process. In other words, the sum of the entropy change of the system and surroundings for any spontaneous process is always greater than zero. Consider the process of an ice cube (say 1.0 mole) melting in your hand, which is at body temperature (37 0 C = 310 K).

The heat lost by your hand is equal to the heat gained by the ice, but has the opposite sign: x 10 3 J/mol So, the entropy change for the surroundings is: ΔS surr = q rev /T = (1 mole)( x 10 3 J/mol) 310 K = J/K Thus, the total entropy change is positive: ΔS total = ΔS sys + ΔS surr = (22.0 J/K) + ( J/K) = 2.6 J/K

Any irreversible process results in an overall increase in entropy, whereas a reversible process results in no overall change in entropy to the Universe. This is basically The Second Law of Thermodynamics: reversible process: ΔS univ = ΔS sys + ΔS surr = 0 irreversible process: ΔS univ = ΔS sys + ΔS surr > 0 But, all spontaneous (real) processes are irreversible (reversible processes being an idealization). Therefore, the total entropy of the Universe increases in any spontaneous process!

The Second Law of Thermodynamics defines the essential character of any spontaneous change as always accompanied by an overall increase in entropy (disorder). In the rusting of a shiny new nail (spontaneous process) there is an increase in the order of the system or a decrease in entropy (ΔS sys ): 4Fe (s) + 3O 2(g)  2Fe 2 O 3(s) + heat ΔS sys < 0 (negative) But, the entropy of the surroundings must increase, and that increase must be larger than the entropy decrease of the system.

So, the moral of the story is the coined phrase for the Second Law of Thermodynamics: “You can’t break even!”  Something is always lost to the Universe as it gains entropy (disorder). Either the ordered structure of matter or energy.