A body cools in 7 minutes from 60°C to 40°C. The temperature of the surrounding is 10°C. The temperature of the body after the next 7 minutes will be

A body cools from $$60°\text{C}$$ to $$40°\text{C}$$ in $$7$$ minutes and the surrounding temperature remains at $$10°\text{C}$$, so we wish to determine its temperature after the next $$7$$ minutes.

According to Newton’s Law of Cooling in exponential form, the temperature at time $$t$$ satisfies the relation $$T(t) - T_s = (T_0 - T_s)\,e^{-kt}$$ where $$T_s = 10°\text{C}$$ is the ambient temperature.

By setting $$t = 7$$ minutes and using the initial drop from $$60°\text{C}$$ to $$40°\text{C}$$, we substitute into the formula to obtain $$40 - 10 = (60 - 10)\,e^{-7k}$$, which simplifies to $$30 = 50\cdot e^{-7k}$$ and hence $$e^{-7k} = \dfrac{3}{5}$$.

For the subsequent $$7$$ minutes, the temperature $$T$$ starting from $$40°\text{C}$$ satisfies $$T - 10 = (40 - 10)\,e^{-7k}$$. Substituting the value $$e^{-7k} = \dfrac{3}{5}$$ yields $$T - 10 = 30 \times \dfrac{3}{5} = 18$$, so $$T = 18 + 10 = 28°\text{C}$$.

Therefore, the temperature after the next $$7$$ minutes is 28°$$\text{C}$$.