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# A body in a room cools from ${85}^{\circ }\text{c}$  to  ${80}^{\circ }\text{c}$ in 5 minutes. The time taken to cool from ${80}^{\circ }\text{c}$  to  ${75}^{\circ }\text{c}$ is

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a
5 minutes
b
<5 minutes
c
>5 minutes
d
either less or more than five minutes.
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detailed solution

Correct option is C

θ1=85∘c    θ2=80∘cθ2=80∘c    θ3=75∘ct1=5 minutest2=?θ0=constant=temperature of surrounding  from newton law of cooling  dθdt1=-kθ1+θ22-θ0---(1)  substitute given values in above equationθ1-θ25=-k85+802-θ085-805=-k82.52-θ055=-k41.25-24---(2)∵Room temperature is 24°C  second part of question, given values substitute in eqn(1)80-75t2=-k80+752-θ05t2=-k38.75-24---(3)  eqn(2) ÷eqn(3)  t2= 5.47mint2is more than 5 minutes

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