Beer Cooler
Beer Cooler
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On a day in which the temperature is 35 Celcius, bottle of Root Beer is taken from a cooler which has a temper?
On a day in which the temperature is 35 Celcius, bottle of root beer is taken from a cooler which has a temperature of 1 degrees Celcius. After 10 minutes the root beer has warmed to a temperature of 12 degrees Celcius. In 16 more minutes its temperature will be??
i cant figure this out. this is a differential equation problem btw.
the temperature difference between the root beer and the ambient temperature will decrease in accordance with an exponential curve at a rate controlled by a "time constant".
Tamb -Trb =Tdelta
Tdelta = 34(e^-t/tau)
Tdelta/34 = e-t/tau
34/Tdelta = e^t/tau
t = time in minutes
tau = time constant in minutes
if we took the natural log of both sides of the equation, we get
ln(34/Tdelta) = t/tau
tau = t/ln(34/Tdelta)
we know that after t = 10 min. Tdelta = 23
tau = 10/ln(34/23) = 10/0.3909 = 25.58 min
after 16 more minutes, t = 26
which is approx equal to tau
t/tau = ln(34/Tdelta)
.984 = ln(34/Tdelta)
e^.984 = 34/Tdelta
2.674 = 34/Tdelta
Tdelta = 12.71Celcius