Question

state Newton's law of cooling show that log (T2 - T1) = -KT + c​

Answer 1

Answer:

By newton's law of cooling the temperature is given as

$ln(\frac{T_2 - T_c}{T_1 - T_c}) = - kt$

Explanation:

As per Newton's law of colling we know that the rate of cooling of a given substance is directly proportional to the difference of the temperature of the object with its surrounding

so we have

$-\frac{dT}{dt} = k(T - T_c)$

so we have

$\int \frac{dT}{T - T_c} = - \int k dt$

now we have

$ln (T - T_c) = - kt$

from temperature T2 to T1 we have

$ln(\frac{T_2 - T_c}{T_1 - T_c}) = - kt$

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Topic : Newton's law of cooling

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