What was the temperature of the object?

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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.
 

Answers and Replies

  • #2
Bystander
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Rewrite Newton in terms of delta T and see if that gives you any ideas.
 
  • #4
HallsofIvy
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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.
 
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I got it! Thanks everyone for the help!
 

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