Question

If the time taken by a cup of tea to cool from 85 degree C to 75 degree C is 1 minute, then the time taken by it to cool from 65 degree C to 55 degree C is

Answer 1

k(80) is the average temperature between 85 and 75 and k(60) is the average temperature between 65 and 55

Answer 2

Given :

The time taken by a cup of tea to cool from $85 ^oC$ to $75 ^oC$ is 1 minute .

To Find :

Time taken by it to cool from $65 ^oC$ to $75 ^oC$ .

Solution :

We know , relation between change in temperature and time is given by :

$\dfrac{T_f-T_i}{Time}=K(\dfrac{T_f + T_i}{2})$

Putting the given condition we get :

$\dfrac{85-75}{1}=K(\dfrac{85 + 75}{2})\\\\K=\dfrac{10}{80}\\\\K=0.125$

Therefore ,

$\dfrac{T_f-T_i}{Time}=0.125\times (\dfrac{T_f + T_i}{2})$

Putting second condition in above equation we get :

$\dfrac{65-55}{Time}=0.125\times (\dfrac{65 + 55}{2})\\\\\dfrac{10}{Time}=6.25\\\\Time=\dfrac{10}{6.25}\\\\Time = 1.6\ min\\\\Time = 1\ min \ 36\ sec$

Therefore , the time taken by it to cool from 65 degree C to 55 degree C is 1 min 36 sec .

Learn More :

Thermodynamics

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