Having Trouble with Two Unknown Equations

[dannypat123]

Hey there,

I'm currently working on a problem that requires you to determine two unknown variables in Newtons Law of Cooling formula. It states that dT/dM = -k(T-To) where dT/dM is the instantaneous rate of cooling, k is an unknown positive constant, T is the temperature of a cup of tea and To is the temperature outside.

In a former question, it is found that -2 and -1.2, are the instantaneous rates of cooling when the tea's temperature is 67 and 60 respectively. Is it possible to determine the constant K and the outside temperature with the information given?

-2 = -k(67-To)
-1.2 = -k(60-To)

Thanks so much!

 

[Harry_the_cat]

Expand first:
-2=-67k+kT .....(1) .....................note: I've used T instead of To for simplicity
-1.2=-60k +kT .....(2)
Subtract eqtn (1) from (2):
0.8=7k
Can you go from there?

 

[dannypat123]

Thanks heaps, I've isolated the K. Would I then do the same process for T or subsitute K into one of the formulas?

Cheers

 

[Harry_the_cat]

Probably easier just to substitute k into one of the formulas. Then substitute it in the other equation to check your answer.