Chapter 9 Reaction Energetics
9.6THE SECOND LAW OF THERMODYNAMICS
We now combine
S and Δ
H into one thermodynamic property that can be used to predict Δ
spontaneity. We begin by realizing that processes that increase the number of ways in which energy can be distributed are statistically favored, but processes affect the entropy of both the system and its surroundings, and it is the disbursal of energy in both that is important. Indeed, the
second law of thermodynamics
defines spontaneity in terms of the
entropy change in the universe.
The entropy of the universe increases (ΔSuniv> 0) in all spontaneous processes.Spontaneous processes are those that increase the entropy of the universe. Processes that reduce the entropy of a
system
can occur spontaneously, but only if they increase the
entropy of the surroundings more than they
decrease the entropy of the system. In
Example 9.7, we show why heat flows spontaneously only from hot to cold. Example 9.7
Show that heat flows spontaneously from a hot reservoir to a cold one.T^1T^2qThe two heat sources at temperatures Tand T 1in the figure in the margin are in thermal 2contact but are insulated from the rest of the universe. Heatcan flow spontaneously fromT^1
to Tonly if the process increases the entro 2py of the universe. Because the twocontainers are insulated from their surroundings, they form their own universe, and we can write:ΔSuniv=ΔS+ 1ΔS> 0. 2SΔand 1SΔare the entropy changes in the two co 2ntainers caused by the flow of heat.Using Equation 9.5, we can write:ΔS= -q/T 1and 1ΔS= +q/T 2(^2)
The negative sign indicates that heat is
leaving the reservoir at temperature T
, and the 1
positive sign indicates that heat is
entering the reservoir at temperature T
. Substitution of 2
theseS values into the ΔSΔ
univexpression yieldsuniv1221qq11S= -+= qTT⎛⎞TTΔ⎜⎟⎝⎠SΔ
univcan be positive only if T> T 1. Thus, heat flows spontaneously from hot to cold as a 2
consequence of the secondlaw of thermodynamics.© byNorthCarolinaStateUniversity