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It takes 10 minutes to cool a liquid fro...

It takes `10 minutes` to cool a liquid from `61^(@)C` to `59^(@)C`. If room temperature is `30^(@)C` then find the time taken in cooling from `51^(@)C` to `49^(@)C`.

A

`4` minute

B

`6` minute

C

`5` minute

D

`8` minute

Text Solution

Verified by Experts

Rate of cooling `alpha` difference in temperature
`(dT)/(dt) prop Delta theta rArr (dT)/(dt)=KDelta theta`
`dT=KDelta theta.dt`
In first case :
`dT=61-59=2`
`Deltatheta=60^(@)-30^(@)=30^(@)`
`dt=4"minute"`
`:. K=(dT)/(Deltatheta dt)=(2)/(30xx4)=(1)/(60)`
For second case :
`dT=2`
`Deltatheta=50-30=20`
`:. dt=(dT)/(KDeltatheta)=(2)/(.^(1)//_(60)xx 20)=6min`
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