Newton's Law of Cooling
Key Questions

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 constantThe 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
#k# .The average coffee temperature at a particular coffee shop is
#75˚# C. Marie purchases a coffee from the local coffee shop. After 10 minutes, the drink has cooled to#67˚# C. The temperature outside the coffee shop is steady at#16˚C# . Assuming the coffee follows Newton's Law of Cooling, determine the value of the constant#k# 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!

Answer:
Newton's Law of Cooling :
#(dT//dt) prop DeltaT#
#=>(d theta //dt) prop Deltatheta# Explanation:
Newton's Law of Cooling states that, if the temperature 'T' of the body is not very different from that of the surroundings '
#T_0# ', then rate of Cooling '(dT/dt)'or'#(d theta//dt)# ' is proportional to the temperature difference between them.