## A thermometer is taken from a room where the temperature is 20◦C to the outdoors, where the temperature is 5◦C. After one minute the t

Question

A thermometer is taken from a room where the temperature is 20◦C to the

outdoors, where the temperature is 5◦C. After one minute the thermometer reads 12◦C.

(a) What will the reading on the thermometer be after one more minute?

(b) When will the thermometer read 6◦C?

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Math
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2022-01-06T05:56:46+00:00
2022-01-06T05:56:46+00:00 1 Answer
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## Answers ( )

Answer:a) : at time t = 2 minutes the temperature will be 8.265 degress

b) : the temperature will be 6 degrees at time t = 3.55 minutes.

Step-by-step explanation:When dealing with temperature changes, it’s best to work with Newton’s Law of Cooling.

here:

: the temperature in the room.

: ambient (or outdoor) temperature (that always remains constant, in our case: )

: are constants

Our conditions are provided:

1)

2)

using the first condition

using the second condition:

we can use our calculated value of C to find k

Finally we can put these constants back in the main equation:

or

a) Reading after one more minute?so it’s asking:

T(2) = ?

Hence, after one more minute the temperature of the room will be 8.267 degrees

b) When will it be 6 degrees?T(t) = 6?

Hence at t = 3.55 minutes the temperature of the room will be 6 degrees.