A thermometer is taken from a room where the temperature is 18°C to the outdoors, where the temperature is -13°C. After one minute the thermometer | reads 2° C. (a) What will the reading on the thermometer be after 4 more minutes? (b) When will the thermometer read -12°C? minutes after it was taken to the outdoors.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
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Question
A thermometer is taken from a room
where the temperature is
18°C to the outdoors, where the temperature is
-13°C. After one minute the thermometer
reads
2° C.
(a) What will the reading on the thermometer be
after
4 more minutes?
(b) When will the thermometer read
-12°C?
minutes after it
was taken to the outdoors.
Transcribed Image Text:A thermometer is taken from a room where the temperature is 18°C to the outdoors, where the temperature is -13°C. After one minute the thermometer reads 2° C. (a) What will the reading on the thermometer be after 4 more minutes? (b) When will the thermometer read -12°C? minutes after it was taken to the outdoors.
Expert Solution
Step 1

By Newton's Law of cooling, it is known that, Tt=Ts+Cekt where Tt is the temperature after t minutes and  Ts is the  temperature of the surroundings.

Here, Ts=-13°C.

The initial temperature on the thermometer is 18°C. That is, T0=18°C.

Therefore, 

T0=Ts+Cek018=-13+CC=18+13=31

That is, C=31.

 

 

 

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