Question

A body cools from \(60\degree C\) to \(40\degree C\) in 6 minutes. If, temperature of surroundings is \(10\degree C\). Then, after the next 6 minutes, its temperature will be ______\(\degree C\).

Hint:

For Newton’s Law of Cooling:
• Use average temperatures for consistent calculations.
• Ensure accurate time intervals and surrounding temperature values.

Answer 1

Correct Answer: 28

1. Newton’s Law of Cooling: Average rate of cooling:

   \[ \frac{T - T_s}{\Delta t} = k(T - T_s), \]

   where \(T_s\) is the surrounding temperature.
2. First Interval:

   \[ \frac{60 - 40}{6} = k\left(\frac{60 + 40}{2} - 10\right), \]

   \[ k = \frac{20}{6 \times 50}. \]

3. Second Interval:

   \[ \frac{40 - T}{6} = k\left(\frac{40 + T}{2} - 10\right). \]

   Solve:

   \[ T = 28^\circ \text{C}. \]

Final Answer: 28°C