Newton's law of cooling practice problems
Newton's law of cooling: find k from one reading, then predict a temperature or a time. 10 problems with worked solutions; in 10 of them every equation is proved by a computer algebra system.
An object at 72° is placed in a room at 22°. After 15 minutes it has cooled to 62°. Using Newton's law of cooling, find its temperature after 45 minutes and when it reaches 32°.
An object at 110° is placed in a room at 70°. After 5 minutes it has cooled to 100°. Using Newton's law of cooling, find its temperature after 15 minutes and when it reaches 80°.
An object at 145° is placed in a room at -5°. After 10 minutes it has cooled to 95°. Using Newton's law of cooling, find its temperature after 30 minutes and when it reaches 0°.
An object at 50° is placed in a room at 0°. After 10 minutes it has cooled to 40°. Using Newton's law of cooling, find its temperature after 30 minutes and when it reaches 10°.
An object at 62° is placed in a room at 22°. After 5 minutes it has cooled to 42°. Using Newton's law of cooling, find its temperature after 45 minutes and when it reaches 37°.
An object at 97° is placed in a room at 22°. After 10 minutes it has cooled to \frac{313}{4}°. Using Newton's law of cooling, find its temperature after 30 minutes and when it reaches 32°.
An object at 80° is placed in a room at 0°. After 20 minutes it has cooled to 64°. Using Newton's law of cooling, find its temperature after 30 minutes and when it reaches 10°.
An object at 172° is placed in a room at 22°. After 20 minutes it has cooled to 97°. Using Newton's law of cooling, find its temperature after 45 minutes and when it reaches 32°.
An object at 97° is placed in a room at 22°. After 10 minutes it has cooled to 82°. Using Newton's law of cooling, find its temperature after 30 minutes and when it reaches 37°.
An object at 150° is placed in a room at 70°. After 15 minutes it has cooled to 130°. Using Newton's law of cooling, find its temperature after 45 minutes and when it reaches 80°.