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If the time taken by a hot body to cool ...

If the time taken by a hot body to cool from 50°C to 40°C is 10 min when the surrounding temperature is 25°C, then the time taken for it to cool from 40°C to 30°C when the surrounding temperature is 15°C, is

A

40 min

B

10 min

C

5 min

D

15 min

Text Solution

Verified by Experts

The correct Answer is:
B
We know that,
`(dQ)/( dt) prop [ (theta_1 + theta_2)/(2) - theta_0]`
`(10)/(10) prop [ (50-40)/(2) - 25]`
`(10)/(10) prop [45-25]" "...(i)`
Similarly,
`(10)/(t) prop [ (40+30)/(2) - 15 ]`
`(10)/(t) prop [35-15] " "...(ii)`
Now, divide Eq. (i) by Eq. (ii), we get
`(t)/( 10) = (20)/(20)`
`t =10` min
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