a pan filled with hot food cools from 94c to 86c in 2minetes when the room temperature is at 20c how long will it take to cool from 71c to 69c
Answer (1)
Student Expert
20th May, 2021
Hi Aspirant!
It is given that the pan cools down from 94 degrees to 86 degree celcius in 2 minutes and the room temperature is 20 degree celcius.
So, T1 = 94 degrees
T2 = 86 degrees
T3 = 20 deg.
t' = 2 min (94 to 86 degrees)
t = ? (from 71 to 69 degrees)
So, as we know:
ln [ (T2-T3)/(T1-T3)] = - kt
=> ln [ ( 86 - 20) / ( 94-20) = -2k
after solving, we get k = - (1/2) ln ( 33/31)
Then , to find 't':
ln [(69-20)/ (71-20)] = -(1/2) ln ( 33/31) t
we get, t = [ln(49/51)] / [-(1/2) ln ( 33/31)]
=> t = 0.69 minutes
=> t = 0.69 x 60 = 41.4 seconds
So, it will take 41.4 seconds to cool down the pan from 71 degrees to 69 degrees celcius.
Thankyou!
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