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Newton's law of cooling states that the ...

Newton's law of cooling states that the rate of change of the temperature T of an object is proportional to the difference between T and the (constant) temperature `tau` of the surrounding medium, we can write it as `(dT)/(dt) = -k(T - tau) k gt 0` constant
An cup of coffee is served at `185^(@)F` in a room where the temperature is `65^(@)F`. 2 minutes later the temperature of the coffee has dropped to `155^(@)F`.
`log_(e)3 = 1.09872, log_(e).(3)/(4) = 0.2877`
Temperature of coffee at time t is given by

A

`tau e^(-k) + [ T(0)] e^(-2k)`

B

`tau e^(k) + [T(0) - tau] e^(-2k)`

C

`tau+[T(0) - tau] e^(-2k)`

D

`tau + 2[T(0)+tau] e^(-)`

Text Solution

Verified by Experts

The correct Answer is:
C
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