Asmall metal bar, whose initial temperature was 20°C, is dropped into a large container of boiling water. How long will it take the bar to reach 90°C if it is known that its temperature increases 2°in 1 second? How long will it take the bar to reach 98°C?

a) 35 s

b) 39 s

Explanation:

Initial temperature T₁ = 20 °C

Final temperature T₂ = 90 °C

Temperature rise rate = 2 °C/s

To solve the problem we can use the formula T₁ + t * 2°C/s = T₂

Where t is the time, in seconds.

We solve for t:

20°C + t * 2°C/s = 90°C

t * 2°C/s = 70°C

t = 35 s

We use the same formula in order to solve the second question, keeping in mind that in this case T₂ = 98 °C:

20°C + t * 2°C/s = 98°C

t * 2°C/s = 78°C

t = 39 s