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

Options

A. `4` minute
B. `6` minute
C. `5` minute
D. `8` minute

Explanation

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`