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Hot water cools from 60^@C to 50^@C in t...

Hot water cools from `60^@C` to `50^@C` in the first 10 min and to `42^@C` in the next 10 min. The temperature of the surrounding is

A

`10^@ C`

B

`15^@ C`

C

`20^@ C`

D

`25^@C `

Text Solution

Verified by Experts

The correct Answer is:
A
By Newton.s law of cooling, Rate of loss of heat = K `xx` mean difference in temperature. In first case,
`(60-50 )/(10) =K ((60+ 50 )/( 2) - theta)`
`implies 1=K (55- theta)`
From eq . (I ) and (ii) `(8)/( 10 ) = ( 46 - theta)/( 55- theta)`
`implies 4/5 =((46- theta))/( ( 55- theta)) implies 4 ( 55 - 0 ) = 5( 46 - theta)`
`implies 220- 4 theta = 230 - 5 theta implies theta = 10^@ C `
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