Question

Temperature of hot soup in a bowl goes 98°C to 86°C in 2 minutes. The temperature of surrounding is 22°C. Find the time taken for the temperature of soup to go from 75°C to 69°C. (Assume newton's law of cooling is valid)

(1) 4.4 minute.
(2) 3.6 minute.
(3) 6.2 minute.
(4) 1.4 minute.

Answer 1

(4) 1.4 minute

Using Newton's law of cooling, Rate of change in temperature, R = dT/dt = -k(T - T_s), T = \(\frac{T_i+T_f}{2}\) 

Divide (i) & (ii)