Question

INTERMEDIATE LEVEL
7. A piece of metal is heated to 428 °C before it is left
to cool. The temperature of the metal falls at als
rate of 23 °C per minute for the first 3 minutes,
6.
V at a rate of 15 °C per minute for the next 15 minutes
go and then at a rate of 8 °C per minute until it reaches
room temperature of 25 °C. Find 2650
(i) the temperature of the metal after 9 minutes.
(ii) the total time needed for the metal to reach a
temperature of 25 °C from 428 °C.​

Answer 1

Temperature drops 23C*3 or 69C in 3 minutes

15C per minute for the next 15 minutes, so that would be 90C in 6minutes for a total drop of 159C in 9 minutes.

 

i. 428-159=269 C

ii 3 minutes, drops 69 C, 15 minutes, drops 225 C, leaving 134 C as temp after 18 minutes. It is 109 C above 25 C, and it falls 8 C a minute or 109/8 = 13 5/8 minutes more

This requires 31 5/8 minutes or 31m37.5s

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