The correct option is (A) 9 min.
Explanation:
If a body cools from 80°C to 50°C, average temperature of liquid = [{80 + 50} / 2] = 65°C (T – To) = excess temperature = 65 – 20 = 45°C rate of fall of temperature = {(dθ1) / dt} = {(80 – 50) / 5} = (30 / 5) = 6°C/min (1)
If body cools from 60°C to 30°C, average temperature of liquid = {(60 + 30) / 2} = 45°C (T – To) = excess temperature = 45 – 20 = 25°C
Rate of fall of temperature = {(dθ2) / dt} = {(60 – 30) / t} = (30 / t)°C/min (2)
As {(– dθ) / dt} = K(T – To) ---- Newtons law of cooling
∴ from (1), – 6 = K(45)
from (2) {(– 30) / t} = K(25)
∴ Taking ratio [{– 6} / {(– 30) / t}] = {45 / 25}
∴ (t/5) = (45 / 25)
∴ t = {(45 × 5) / 25}
t = 9 min