dbanks701
19.09.2019 •
Mathematics
The temperature of a cup of coffee varies according to newton's law of cooling: , where t is the water temperature, a is the room temperature, and k is a positive constant.
if the coffee cools from 180°f to 100°f in 10 minutes at a room temperature of 75°f, how long (to the nearest minute) will it take the water to cool to 80°f?
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Ответ:
T0 is initial temperature of coffee ---> 180
A = 75
Step 1: Find value for k
plug in T = 100, t = 10 min
This is just as good as finding an actual value for 'k' because it will be subbed into Cooling equation anyway. Subbing in e^(-k) is easier.
Step 2: Find value for 't' when T = 80
Therefore it takes about 21 minutes for coffee to cool from 180 to 80 degrees.
Ответ: