A body cools from a temperature 3t to 2t

Asked by admin @ 12/08/2021 in Physics viewed by 294 People

A body cools from a temperature 3t to 2t in 10 min. The room temperature is t. Assume that newton's law of cooling is applicable. The temperature of the body at the end of next 10 min will be

Answered by admin @ 12/08/2021

Answer:

The temperature of the body at the end of next 10 min will be 3t/2

Explanation:

From newton's law of cooling we know that,

(θ₁ - θ₂)/t = k[(θ₁ + θ₂)/2 - θ₀]

given,

θ₁ = 3t

θ₂ = 2t

t = 10 min

θ₀ = t

hence putting these values in the above formula, we get,

(3t-2t)/10 = k[(3t + 2t)/2 - t]

=> t/10 = 3kt/2

=> k = 1/15

In the next 10 minutes, lets the temperature be θ,

applying the same formula we get,

(2t - θ)/10 = 1/15[(2t + θ)/2 - t]

(2t - θ)/10 = 1/15[θ/2]

=> 6t - 3θ = θ

=> 4θ = 6t

=> θ = 3t/2

Hence the temperature of the body at the end of next 10 min will be 3t/2

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