Newton’s lawof cooling states that the rate ofchange (d T /d t ) inthe temperatu

ID: 1738388 • Letter: N

Question

Newton’s lawof cooling states that the rate ofchange (dT/dt) inthe

temperatureT of a body in a medium of temperatureTmedis proportional to

the difference between thetemperature of the body and the temperature of

the medium. Mathematicallythis law can be represented with

where k > 0 is aconstant of proportionality. The inverse of k has units oftime

and is called thetime constantof the equation. Its value reflects how fastheat

is transferred between theobject in question and the surrounding medium.

The larger (smaller) the timeconstant 1/k, the faster(slower) the rate of heat

transfer.

Dr. Lorenz’s flat ispoorly insulated and in the winter I like to keep thefurnace

running constantly such thatthe temperature is kept at 20°C. However, a

couple of weeks ago, Dr.Lorenz’s furnace broke down at midnight when the

outside temperature was-10°C,and after 30 minutes the temperature inside

of Dr. Lorenz’s flat is9°C.

a. What is the temperature inDr. Lorenz’s flat after 1 hour?

b. How long will it take forthe temperature inside of Dr. Lorenz’s flat todrop

to -5°C?

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