Question

A hot fluid cools from 200°C to 100°C in 5 minutes. Then the time taken by it to cool from 100°C to 50°C is nearly (Room temperature = 30°C)

• A. 2.5 minutes
• B. 5.2 minutes
• C. 6.7 minutes
• D. 9.3 minutes

Hint:

Newton's law of cooling can be used to estimate the time required for a body to cool, depending on the temperature differences.

Answer 1

The Correct Option is C

This is an application of Newton's law of cooling. According to this law, the rate of change of temperature is proportional to the difference between the temperature of the object and the surroundings. The time taken for the temperature change can be found using the formula: \[ \frac{T_1 - T_2}{T_2 - T_3} = \frac{t_1}{t_2} \] Substituting the values for \( T_1 = 200^\circ C \), \( T_2 = 100^\circ C \), \( T_3 = 50^\circ C \), and \( T_s = 30^\circ C \), we find that the time required to cool from 100°C to 50°C is 6.7 minutes.