Page 42 - Bruno Linder Elementary Physical Chemistry

August 18, 2010 11:36 9in x 6in b985-ch03 Elementary Physical Chemistry

The Second Law of Thermodynamics 27

3.3.4. Isolated Systems

Variation of heats is difficult to determine, and most often one calculates
entropy changes of isolated systems, where dq = 0. Thus, for an isolated
system, Eq. (3.18) takes the form
∆S isolated ≥ 0 (3.19)

Comment: The results obtained so far, which relates entropy to heat
change divided by temperature, was derived for a particular system —
an ideal gas. What assurance do we have that the efficiency criterion
applies to other systems? It does! There is a theorem (not to be
developed here) that proves that all systems operating reversibly
between the same temperatures have the same efficiency.Thus,if
we derive the entropy for one system, we have it for all.

3.4. Determination of Entropy
Note: We consider in this section only reversible changes.

3.4.1. Entropy change in Phase Transitions (solid–liquid,
liquid–vapor, solid–vapor)

i) At constant T

∆S = dq/T = q/T (3.20)

ii) At constant T and P, q P =∆H and ∆S =∆H/T (3.21)

Example 3.1.
◦
H 2 O(s, 0 C) = H 2O(l, 0 C) ∆H =6.01 kJmol −1
◦
∆S = 6010J mol −1 /273.15 K = 21.99J K −1 mol −1