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A body cools in 7 minutes from 60^(@)C ...

A body cools in 7 minutes from `60^(@)C` to `40^(@)C`. What will be its temperature after the next 7 minutes? The temperature of the surroundings is `10^(@)C`.

A

`32^(@)C`

B

`28^(@)C`

C

`20^(@)C`

D

`25^(@)C`

Text Solution

Verified by Experts

The correct Answer is:
B
`(d theta)/(dt)=k(theta_(AV)-theta_(0))`
`(20)/(7)=k(50-10)` . . (i)
`(40-theta)/(7)=k((40+theta)/(2)-10)` . . . (ii)
Dividing equation (ii) by (i)
`(40-theta)/(20)=(40+theta-20)/(2xx40)`
`4(40-theta)=theta+20`
`5 theta=160-20`
`theta=(140)/(5)=28^(@)C`.
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