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Certain quantity of water cools from 70^...

Certain quantity of water cools from `70^(@)C` to `60^(@)C` in the first `5` minutes and to `54^(@)C` in the next `5` minutes. The temperature of the surrounding is

A

`45^(@)C`

B

`20^(@)C`

C

`42^(@)C`

D

`10^(@)C`

Text Solution

Verified by Experts

The correct Answer is:
A
According to Newton.s law of cooling
`(theta_(1)-theta_(2))/(t)=k[(theta_(1)+theta_(2))/(2)-theta_(0)]`
`rArr(70-60)/(5)=k[(70+60)/(2)-theta_(0)]`
`2=k[65=-theta_(0)]` …(i)
and
`(60-54)/(5)=k[(60+54)/(2)-theta_(0)]`
`rArr6/(5)=k[57-theta_(0)]` ...(ii)
By dividing Eqs. (i) by (ii) we have
`10/(5)=(65-theta_(0))/(37-theta_(0))rArrtheta_(0)=45^(@)C`
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