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A metal sphere cools from 72^(@)C to 60^...

A metal sphere cools from `72^(@)C` to `60^(@)C` in 10 minutes. If the surroundings temperature is `36^(@)C`, then the time taken by it to cool from `60^(@)C` to `52^(@)C` is

A

8 minutes

B

4 minutes

C

12 minutes

D

10 minutes

Text Solution

Verified by Experts

The correct Answer is:
D
`(d theta)/(dt)=k(theta_(AV)-theta_(0))`
`(12)/(10)=k(66-36)=k30`
`k=(12)/(300)=(1)/(25)`
`((d theta)/(dt))=k (theta_(AV)-theta_0)`
`(8)/(dt)=(1)/(25)(56-36)`
dt=10 min.
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