# What was the temperature of the object?

## Homework Statement

An object is placed in a room where the temperature is 20 degrees Celsius. The temperature of the object drops by 5 degrees Celsius in 4 minutes and by 7 degrees Celsius in 8 minutes. What was the temperature of the object when it was initially placed in the room?

## Homework Equations

Newton's law of cooling: T(t)=Ta+(To-Ta)e^(-kt)

## The Attempt at a Solution

T(t)=Ta+(To-Ta)e^(-kt)
I know that I need to solve for To, which is the initial temperature but I don't know what to do.

Bystander
Homework Helper
Gold Member
Rewrite Newton in terms of delta T and see if that gives you any ideas.

HallsofIvy
Homework Helper

## Homework Statement

An object is placed in a room where the temperature is 20 degrees Celsius. The temperature of the object drops by 5 degrees Celsius in 4 minutes and by 7 degrees Celsius in 8 minutes. What was the temperature of the object when it was initially placed in the room?

## Homework Equations

Newton's law of cooling: T(t)=Ta+(To-Ta)e^(-kt)

## The Attempt at a Solution

T(t)=Ta+(To-Ta)e^(-kt)
I know that I need to solve for To, which is the initial temperature but I don't know what to do.
When t= 4 min, T(4)= Ta+ (To- Ta)e^(-4k)= 15. When t= 8 min, T(8)= Ta+ (To- Ta)e^(-8k)= 13.
What do you get if you subtract e^(-8k)T(4)- e^(-4k)T(8)?

You are asked to find T(0)= To.

• Math10
I got it! Thanks everyone for the help!