Question

# In a room where the temperature is 30∘C a body cools from 61∘C to 59∘C in 4 minutes. The time taken by the body to cool from 51∘C to 49∘C will be about :

A
5 minutes
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B
8 minutes
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C
4 minutes
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D
6 minutes
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Solution

## The correct option is D 6 minutesThe average temperature of the liquid in the first caseθ1=61+592=60∘CTemperature difference from surroundingθ1−θ0=60−30=30∘CThe rate of fall of temperature is−dθ1dt=61∘C−59∘C4=24=12∘C/minFrom Newton's law of cooling12∘C/min=K(30∘)⇒K=160.....(i)In the second case, average temperatureθ2=51+492=50∘CTemperature difference with surroundingθ2−θ0=50∘C−30∘C=20∘CIf it takes a time t to cool from 51∘C to 49∘Cthen −dθ2dt=51−49t=2∘CtFrom Newton's law of cooling2∘Ct=160×20⇒t=6 min

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