Question

A body takes 5 min for cooling from 50°C to 40°C. Its temperature comes down to 33.33°C in the next 5 min. Temperature of the surroundings is

• A. 15°C
• B. 20°C
• C. 18°C
• D. 17°C

Hint:

In Newton's law of cooling, the rate of cooling depends on the difference between the temperature of the object and the surrounding temperature. The temperature of the surroundings can be determined by observing the rate of change in temperature.

Answer 1

The Correct Option is B

The temperature change follows Newton's law of cooling, which is given by: \[ \frac{dT}{dt} = -k(T - T_s) \] where \( T \) is the temperature of the object, \( T_s \) is the surrounding temperature, and \( k \) is the cooling constant. We can use the given temperatures to estimate \( k \) and solve for \( T_s \). From the cooling process, the temperature changes as follows: 1. From 50°C to 40°C, the temperature decreases by 10°C in 5 minutes. 2. From 40°C to 33.33°C, the temperature decreases by 6.67°C in the next 5 minutes. Using the equation of exponential decay for cooling, we can estimate that the surrounding temperature \( T_s \) is 20°C. 
Hence, the correct answer is (b).