Bradley, working in his 23 C kitchen, is cooking himself a crepe in an iron skillet that has a circular bottom with a diameter of .30 m. How hot must the skillet be in order for Bradley to make a 710.3 m^2 crepe that just fills the bottom of the pan?

(coefficient of expansion of iron=
12x10^-6 C^-1)

To find the temperature the skillet must be in order for Bradley to make a crepe that fills the bottom of the pan, we can use the concept of thermal expansion.

The formula for thermal expansion is given as:
ΔL = α * L0 * ΔT

Where:
ΔL is the change in length
α is the coefficient of linear expansion
L0 is the initial length
ΔT is the change in temperature

In this case, we can consider the change in area of the skillet bottom. Since the crepe is going to fill the bottom of the pan, we need to find the change in temperature required for the area of the crepe to be 710.3 m².

First, let's calculate the initial area of the skillet bottom using its diameter:
Radius (r) = diameter / 2 = 0.30 m / 2 = 0.15 m
Initial Area (A0) = π * r² = 3.14 * 0.15² = 0.07065 m²

Now we can calculate the change in temperature (ΔT) required for the crepe area to be 710.3 m²:
Change in Area (ΔA) = Final Area - Initial Area = 710.3 m² - 0.07065 m² = 710.22935 m²

We can rearrange the thermal expansion formula to solve for the change in temperature:
ΔT = ΔA / (α * A0)

Substituting the values:
ΔT = 710.22935 m² / (12x10^-6 C^-1 * 0.07065 m²)
= 710.22935 m² / 8.47949x10^-6
≈ 8.3824x10^7 C

Therefore, the skillet must be heated to approximately 8.3824x10^7 degrees Celsius in order for Bradley to make a crepe that just fills the bottom of the pan.

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