Temperatures, non-proportionality,
and hidden proportionality...

An adventure for Math 541 (Fall 2003, Dr. Barzilai)

Conversion: C = (5/9)·(F-32)

Thus, F = (9/5)C + 32

I) Exercise: 1) explain by logic why F and C are not proportional b) find values for F and C pairs which show that C and F are not proportional.

II) Given two temperatures given in F. Call them F1 and F2.

Then C1 = (5/9)·(F1-32) and C2 = (5/9)·(F2-32)

Thus ΔC = C1 - C2
= (5/9)·(F1-32) - (5/9)·(F2-32)
= (5/9)·[(F1 - 32) - (F2 - 32)]
= (5/9)·[F1 - 32 - F2 + 32]
= (5/9)·[F1 - F2]
= (5/9)·[ΔF]

Thus although C and F measurements (e.g. C1 and F1, etc) are not proportional, we still have that it is true that ΔC and ΔF are proportional.