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In a room where the temperature is 30^(@...

In a room where the temperature is `30^(@)C`, a body cools from `61^(@)C` to `59^(@)C` in 4 minutes. The time (in min.) taken by the body to cool from `51^(@)C` to `49^(@)C` will be

A

4 minutes

B

6 minutes

C

5 minutes

D

8 minutes

Text Solution

Verified by Experts

Rate of coooling `prop` difference in temperature
`(dT)/(dt)prop Delta theta`
`(dT)/(dt)=K Delta thetaimpliesdT=K delta theta dt`
In first case
`dT=61-59=2`
`Delta theta=60-30=30`
`dt=4` minutes
`:.K=(dT)/(Delta theta dt)=2/(30xx4)=1/60`
For second case
`Delta theta=50-30=20 `
`dt=(dT)/(K Delta theta)=2/(1//60xx20)=6` min
Hence b is correct.
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