Section 4.8b:
Newton’s Law
of Cooling
Newton’s Law of Cooling
The temperature u of a heated object at a given time t can
be modeled by:
u(t) = T + (u0 – T)ekt , k < 0
Where T is the constant temperature of the surrounding
medium, u0 is the initial temperature of the heated object
and k is a negative constant.
Newton’s Law of Cooling
An object is heated to 100◦C and is then allowed to cool in a
room whose air temperature is 30◦C.
a) If the temperature of the object is 80◦C after 5 minutes,
when will its temperature be 50◦C?
Newton’s Law of Cooling
An object is heated to 100◦C and is then allowed to cool in a
room whose air temperature is 30◦C.
b) Determine how much time elapses before the object is
35◦C?
Newton’s Law of Cooling
You are baking cookies and want to know how long you have
to wait before they are cool enough to eat. The cookies are
baked in an oven that is 375o. You take them out of the oven
into a room that is 72o. After 3 minutes, the cookies are 325
degrees. The cookies have to cool to 100o in order not to burn
your mouth. How long do you have to wait?
Newton’s Law of Cooling
After spending hours studying for finals, you want an ice pop.
Unfortunately, you do not have any at your house so you go
to Target. Unfortunately, all the pre-frozen ice pops were sold
and only the unfrozen ones are left. You decide to buy the
box and chill them at home. When you get home, the ice
pops are 76◦F and you put them in your
freezer which stays at a constant
temperature of 0◦F. After 10 minutes,
the temperature of the ice pops have
cooled to 65◦F. If you have to wait until
the ice pops are 25◦F to enjoy them,
how much longer must you wait to
enjoy your ice pops?
Section 4.8b:
Newton’s Law of Cooling
Homework:
Pages 334 – 335
#11a, 12a, 13ac, 14abd, 15a,
16 (no graph), 19 & 20