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Water at 60^(@)C cools to 50^(@)C in the...

Water at `60^(@)`C cools 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)`
In second case `( 50 - 42)/(10) = K ( (50 + 42)/(2) - theta)`
`implies (8)/(10) = K ( 46 - theta)`
From Eqs . (i) and (ii) `(8)/(10) = ((46 - theta))/((55- theta))`
`implies (4)/(5) = ((46-theta))/((55 - theta)) `
`implies 4 (55 - theta) = 5 ( 46 - theta)`
`implies 220 -4 theta = 230 - 5 theta`
`implies theta = 10^(@) C `
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