A hot body placed in air cools down to a lower temperature. The rate of decrease of temperature is proportional to the temperature difference from the surrounding. The body loses 60 % and 80 % of maximum heat it can loose in time t₁ and t₂ respectively. The ratio t₂ / t₁ will be

Step-by-step solution

According to Newton's law of cooling, - d T d t T or d T d t =-K T Solved the above Eq., we get aligned T(t) & =T₀+ (T₁-T₀ ) e^ -k t e^ -k t = T(t)-T₀ T₁-T₀ or t & = 1 k T₁-T₀ T(t)-T₀ aligned Where, T₁= temperature of body at t=0T₀= temperature of surrounding. Let T₁=0^ C So, t= 1 k -T₀ T(t)-T₀ = 1 k -Q₀ Q(t)-Q₀ [ Q(t)=m c T(t)] According to the question, the body loses 60 % and 80 % of maximum heat in time t₁ and t₂ then aligned t₁ & = 1 k ( -Q₀ 60 100 Q₀-Q₀ ) t₂ & = 1 k ( -Q₀ 80 100 Q₀-Q₀ ) aligned Divide Eqs. (i