A bucket full of hot water is kept in a room. It cools from 75oC to 70oC in T1 minutes, from 70oC to 65oC in T2 minutes and from 65oC to 60oC in T3 minutes. Which of the following relation is correct?
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Correct option is B)
By Newton's law of cooling θ2−θ1dθ2=kdt where k is inversely proportional to product of mass and specific heat of the water, θ1 and θ2 are surrounding and average water temperatures and dt is the time interval. given that for case (i) dθ2=75oC−70oC=5oC, θ2=275+70=72.5oC, dt=T1 θ2−θ1dθ2=kdt72.5−θ15=kT1T1=k(72.5−θ1)5 case (ii) dθ2=70oC−65oC=5oC, θ2=270+65=67.5oC, dt=T2 θ2−θ1dθ2=kdt67.5−θ15=kT2T2=k(67.5−θ1)5 case (iii)dθ2=65oC−60oC=5oC, θ2=265+60=62.5oC, dt=T3 θ2−θ1dθ2=kdt62.5−θ15=kT3T3=k(62.5−θ1)5 by comparing above three cases T1<T2<T3 option (B) is the correct answer
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