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

<p>Newton&#39;s law of cooling states that the rate of heat loss of a body is directly proportional to the difference in the temperatures between the body and its surroundings. The average rate of cooling can be represented as:</p> <p>$\frac{T_1-T_2}{t} = K \left(\frac{T_1+T_2}{2} - T_s\right)$</p> <p>where:</p> <ul> <li>$T_1$ and $T_2$ are the initial and final temperatures of the body,</li> <li>$t$ is the time it takes for the body to cool from $T_1$ to $T_2$,</li> <li>$T_s$ is the temperature of the surroundings, and</li> <li>$K$ is a constant of proportionality.</li> </ul> <p>In the first 7 minutes, the body cools from $60^\circ C$ to $40^\circ C$, and the surrounding temperature is $10^\circ C$. So, the first equation is:</p> <p>$\frac{60-40}{7} = K \left(\frac{60+40}{2} - 10\right) \tag{1}$</p> <p>In the next 7 minutes, the body cools from $40^\circ C$ to $T^\circ C$, with the same surrounding temperature. So, the second equation is:</p> <p>$\frac{40-T}{7} = K \left(\frac{40+T}{2} - 10\right) \tag{2}$</p> <p>Solving equation (1) for $K$ and substituting into equation (2) will give the temperature $T$ after the next 7 minutes:</p> <p>$T = 28^\circ C$</p>