At 3 p. m., a hot coal was pulled out of a furnace and allowed to cool at room temperature (75°F). If, after 10 minutes, the temperature of the coal was 475°F, and after 20 minutes, its temperature was 395°F, find the following.

(a) The temperature of the furnace.

°F

(b) The time when the temperature of the coal was 105°F. (Round your answer to the nearest minute.)

: p. m.

Question

Diet Coke

Physics

7 June, 18:35

At 3 p. m., a hot coal was pulled out of a furnace and allowed to cool at room temperature (75°F). If, after 10 minutes, the temperature of the coal was 475°F, and after 20 minutes, its temperature was 395°F, find the following.

(a) The temperature of the furnace.

°F

(b) The time when the temperature of the coal was 105°F. (Round your answer to the nearest minute.)

: p. m.

+5

Answers (1)

Know the Answer?

Megan Bean · Answer 1

A. This can be solved using Newton's Law of Cooling

T - To = (Tb - To) e^kt

From the given conditions

T = 475 F

To = 75 F

t = 10 min

475 - 75 = (Tb - 75) e^k (10)

For the second condition

T = 395 F

To = 75 F

t = 20 min

(395 - 75) = (Tb - 75) e^k (20)

There are two unknowns and two equations, solve for

k and Tb

You can then use this to solve for the time until the T = 105 F