Question

A liquid contained in a calorimeter cools from 80°C to 60°C in 10 mins. If the temperature of the surroundings is 30°C, calculate time it will take to cool further to 45°C?

Answer 1

According to Newton's law of cooling, we have

mc (T₁ - T₂)/t = k [(T₁ + T₂)/2 - T₀)] ---------------(1)

mc/k = [(T₁ + T₂)/2 - T₀)]/[(T₁ - T₂)/t]

mc/k = [(80+60)/2 - 30)]/[(80 - 60)/10]
= 20

Substituting T1 = 60 and T2 = 45 and T0 = 30 (all in °C) in Eq. (1), we get

mc (60 - 45)/t = k [(60+ 45)/2 - 30)]
15 mc/t = 22.5 k
t =15 mc/(22.5k)
= (15/22.5) x (20)
= 13.33 min

The body takes 13.33 min to cool from 60°C to 45 °C.