How do I find #k# in Newton's Law of Cooling?
1 Answer
Answer:
Set up an equation with all the knowns and solve for the unknown! Make sure to know your law of cooling too, shown in blue in the Explanation section.
Explanation:
Newton's Law of Cooling is given by the formula
#color(blue)(T(t) = T_s + (T_0 - T_s)e^(-kt)#
Where
•
#T(t)# is the temperature of an object at a given time#t#
•#T_s# is the surrounding temperature
•#T_0# is the initial temperature of the object
•#k# is the constant
The constant will be the variable that changes depending on the other conditions. Let's take an example of a question where you would need to find
The average coffee temperature at a particular coffee shop is
Let's identify our variables.
•
#T_0 = 75˚C#
•#T_s = 16˚C#
•#t = 10#
•#T(t) = 67˚C#
•#k = ?#
We have
#67 = 16 + (75 - 16)e^(-10k)#
#51 = 59e^(-10k)#
#51/59 = e^(-10k)#
#ln(51/59) = ln(e^(-10k))#
#ln(51/59) = -10k#
#k = -1/10ln(51/59)#
Use a calculator to get
#k~~ 0.01457#
Hopefully this helps!