While I was drinking my coffee this morning the thought occurred to me: how much faster does my coffee cool with the spoon in it?
So I did a rough estimation with the following assumptions:
- All cooling was done through natural convection following Newton’s Law of Cooling, with a convective heat transfer value of h=40 W/(m^2*K) and a bulk air temperature of 294 K (~70 F)
- The thermal conductivity of the coffee mug and the spoon are that of ceramic (k=1.5 W/(m*K)) and stainless (k=16 W/(m*K)) respectively
- The spoon has uniform temperature along it length equal to that of the bulk coffee
- The coffee cup is a cylinder with height of 4 inches and a diameter of 3.5 inches
- The spoon has a total length of 8 inches with heat transfer only occurring off the section of the handle emerging from the coffee
- Coffee has the same heat capacity and density as water
- Coffee is produced from the pot and poured into the cup at 355 K (~180 F)
- No heat is lost through evaporation of the coffee
And here are the results:
Blue represents the standard coffee.
Yellow is the coffee with spoon.
Red horizontal is safe drinking temperature (333 K).
Purple Horizontal is air temperature.
What can be gathered is the coffee with spoon hits the safe drinking temperature almost a full 150 seconds (2.5 minutes) sooner than the standard coffee.
This is not a life changing amount of time saved but it’s 2.5 more minutes of WordPress everyday.