A body cools from 50 ° C to 40 ° C in 5 minutes. Its temperature comes down to 33 . 33 ° C in the next 5 minutes. The temperature of the surroundings is

Step-by-step solution

Let θ 0 = temperature of surrounding, Using Newton's law of cooling, log   θ 2 - θ 0 θ 1 - θ 0 = - K t log 40 - θ 0 50 - θ 0 =   - K × 5 .....(i) log 33.33 - θ 0 40 - θ 0   =   - K × 5 .....(ii) From Eqs.(i) and (ii), 40 - θ 0 50 - θ 0     =   33.33 - θ 0 40 - θ 0 On solving, we get θ 0 = 19 .95 ° C   ≈ 20   ° C