Question

The temperature of a body in air falls from \( 40^\circ \text{C} \) to \( 24^\circ \text{C} \) in 4 minutes. The temperature of the air is \( 16^\circ \text{C} \). The temperature of the body in the next 4 minutes will be:

• A. 28/3 °C
• B. 14/3 °C
• C. 56/3 °C
• D. 42/3 °C

Hint:

Use Newton's Law of Cooling to calculate temperature changes over time. The rate of temperature change depends on the difference between the object's temperature and the surrounding temperature.

Answer 1

The Correct Option is A

This problem utilizes Newton's Law of Cooling, represented by the differential equation: \[ \frac{dT}{dt} = -k(T - T_{\text{air}}), \] where \( T \) denotes the body's temperature, \( T_{\text{air}} \) is the surrounding air temperature, and \( k \) is a proportionality constant. The temperature decreases from \( 40^\circ \text{C} \) to \( 24^\circ \text{C} \) over a period of 4 minutes. By employing Newton's Law of Cooling, we can determine the value of the constant \( k \). Subsequently, this constant can be used to calculate the temperature change during the subsequent 4 minutes. Following the given data and performing the required calculations, the temperature after an additional 4 minutes will be:

Final Answer: