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 involves Newton's Law of Cooling, which can be expressed as: \[ \frac{dT}{dt} = -k(T - T_{\text{air}}), \] where \( T \) is the temperature of the body, \( T_{\text{air}} \) is the ambient temperature (temperature of the air), and \( k \) is a constant. The temperature changes from \( 40^\circ \text{C} \) to \( 24^\circ \text{C} \) in 4 minutes. Using Newton's Law of Cooling, we can compute the constant \( k \) and then apply it to determine the temperature change in the next 4 minutes. Based on the given information and applying the necessary calculations, the temperature after 4 more minutes is: 

Final Answer: