Question

In a surrounding medium of temperature of 1$0^{\circ }C$, a body takes $7$ min for a fall of temperature from ${60}^{\circ }C$ to ${40}^{\circ }C$. In what time the temperature of the body will fall from ${40}^{\circ }C$ to ${28}^{\circ }C$?

• A. 7 min
• B. 11 min
• C. 14 min
• D. 21 min

Answer 1

Answer: (A)

7 min

Newton’s Law of Cooling states that the rate fall of temperature of the body is proportional to the difference between the temperature of the body and that of the surrounding medium.

Thus $\frac{{\theta }_2-{\theta }_1}{t}=K(\frac{{\theta }_1+{\theta }_2}{2}-{\theta }_0)$

$⟹\frac{60-40}{7}=K(\frac{60+40}{2}-10)$

and $\frac{40-28}{t}=K(\frac{40+28}{2}-10)$

Solving the two equations gives $t=7min$