10-2.Transmission of Heat
medium

A body cools in $7$ minutes from $60^{\circ}\,C$ to $40^{\circ}\,C$. The temperature of the surrounding is $10^{\circ}\,C$. The temperature of the body after the next $7$ minutes will be

A

$32^{\circ}\,C$

B

$30^{\circ}\,C$

C

$28^{\circ}\,C$

D

$34^{\circ}\,C$

(JEE MAIN-2023)

Solution

using average rate of Newton's law of cooling

$\frac{T_1-T_2}{t}=K\left(\frac{T_1+T_2}{2}-T_s\right)$

Given $\frac{60-40}{7}=K(50-10) \ldots$ (i)

$\frac{40-T}{7}=K\left(\frac{40+T}{2}-10\right) \ldots$ (ii)

From $(i)$ and $(ii)$

$T =28^{\circ}\,C$

Standard 11
Physics

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