A body is heated to 110^ C and placed in air at 10^ C . After 1 hour its temperature is 60^ C . The additional time required for it to cool to 30^ C is

Step-by-step solution

(D) Let be the temperature of body at time t . Temperature of air is given to be 10^ C . = ₀ (say). aligned & d dt ( - ₀ ) & d dt =- k ( - ₀ ), k >0 & d - ₀ = - kt | - ₀ |=- kt + c ...(1) aligned ( - ₀ c )= e ^ - kt = ₀+ ce ^ - kt When t =0, =110 and ₀=10, =10+100 e ^ - kt 110=10+ c c =100 c When =60^ C , t =1 Substituting value in equation (1), ( 60-10 100 )=- k 1 k =- ( 1 2 ) ( -10 100 )= t ( 1 2 ) When =30^ C , then ( 30-10 100 )= t ( 1 2 ) ( 20 100 )=t 1 2 - 5=-t 2 t= 5 2 Additional time required is 5 2 -1