Question

Suppose you make hot chocolate and it starts off just too hot to drink, so you put it in the freezer temporarily to cool it off. If the original temperature is 190 degrees Fahrenheit and the freezer is 0 degrees Fahrenheit, what will the temperature of the hot chocolate be after 2 minutes? (k = 0.12)

191.27 degrees
189.21 degrees
149.46 degrees
188.73 degrees

Answer 1

After 2 minutes the temperature of the hot chocolate will be 149.46 degrees Fahrenheit.

Explanation:

We are going to use the Newton's law of cooling to solve this exercise. The Newton's law of cooling states that the amount of heat lost by a body is proportional to the difference of temperature between the body and the enviroment. We are going to use the following function :

`T(t)=T_(0)+(T_(i)-T_(0)).e^(-kt)`

Where ''T(t)'' is the temperature of the body that depends of the variable ''t'' which is time.

Where
`T_(0)` is the temperature of the surroundings

In this case
`T_(0)` is the temperature of the freezer

Where
`T_(i)` is the initial temperature of the body which is cooling. In this case,
`T_(i)` is the temperature of the hot chocolate

And where ''k'' is a constant. In this case,
`k=0.12` is a data of the exercise

If we replace all the values in the equation and replacing
`t=2minutes`

⇒

`T(2minutes)=0+(190-0).e^(-(0.12).(2))`

`T(2minutes)=(190).(e^(-0.24))=149.46`

We find that the temperature of the hot chocolate after 2 minutes is 149.46 degrees Fahrenheit