Question

A metal sphere cools from 80 °C to 60
°C in 6 min. How much time with it take
to cool from 60 °C to 40 °C if the room
temperature is 30°C?
[Ans: 10 min]​

Answer 1

Time it would take to cool from 60 °C to 40 °C if the room temperature is 30°C is given as follow :

A metal sphere cools from 80 °C to 60°C in 6 min.

1.Initial temperature ( Ti) = 80°C

Final temperature ( Tf) = 60°C

Temperature of the surrounding ( To) = 30°C

t =6 min

2. A/C to Newton's law of cooling

Rate of cooling ( dT/dt) = K[ (Ti+Tf)/2 - To]

3. (Tf - Ti)/t = K[ ( 80 + 60)/2 - 30]

( 80-60)/5 = K[ 70 - 30]

4 = K×40

4. K = 4/40 = 1/10

5. In second condition,

Initial temperature ( Ti) = 60°C

Final temperature ( Tf) = 40°C

Time taken for cooling is t

6. A/C Newton's law of cooling

( 60 - 40)/t = 1/10 [ (60+40)/2 -30]

20/t = 1/10 × 20

t = 10 min