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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3 weeks 2022-01-06T05:56:46+00:00 1 Answer 0 views 0

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?

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.