A cup of tea cools from 65.5 o C to 62.5 o C in 1 min in a room at 22.5 o C . How long will it take to cool from 46.5 o C to 40.5 o C in the same room?

Step-by-step solution

According to Newton's law of cooling, θ 1 - θ 2 t = α θ 1 + θ 2 2 - θ 0 ∵ α = u n i v e r s a l c o n s t a n t 65.5 - 62.5 1 = α 65.5 + 62.5 2 - 22.5 .....(i) 46.5 - 40.5 t = α 46.5 + 40.5 2 - 22.5 .....(ii) Solving Equations. (i) and (ii), we get t = 4 m i n