IP An aluminum saucepan with a diameter of 23 cm and a height of 6.0 cm is fille

Question

IP An aluminum saucepan with a diameter of 23 cm and a height of 6.0 cm is filled to the brim with water. The initial temperature of the pan and water is 12 C. The pan is now placed on a stove burner and heated to 89 C. Calculate the volume of water that overflows or the drop in water level in the pan, whichever is appropriate. answer in cm^3

I know that since it hasnt reached 100 C nothing has been converted to steam so the water definitely overflows. I tried using change V=3*alpha*initial V*change T and I got an answer of 120.98 cm^3 but that was wrong.

Explanation / Answer

The volume of the pan (and thus, the water) is the area of the pot, which is the area of the circle of the pan, multiplied by its height, or, (h)(p r2) where r = ½ d.
Thus, the volume is:

V = (h)(p r2) = (6.0 cm)(pi)(11.5)2 = (6.0 cm)(3.14)(132.25) = (6.0 cm)(3.14)(132.25) = 2496 cm3.
So, this is the “original” volume, or V0. DT = 89° C – 12° C = 77° C.

Thus, DV(water) = bV0DT = (0.21 x 10- 3 )(2496)(77) = 40.36 cm3.

But the Aluminum pot will expand, too, by:

DV(Al) = 3aV0DT = (3)(2.4 x 10- 5)(2.945 x 10^3)(6.9 x 101) =

(3)(2.4)(2.945)(6.9)(10- 5)(103)(101) = 146.31 x 10- 1. = 14.63 cm3.

Finally, overall change of volume is [DV(water) - DV(Al)] = (40.36) - (14.63) = 25 cm3.

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