A bowl filled with very hot soup cools from 98 ° C to 86^ C in 2 minutes when the room temperature is 22^ C . How long it will take to cool from 75^ C to 69^ C ?

Step-by-step solution

From Newton's law of cooling, we have Δ Q Δ t = - K T avg - T 0 Where, Q = m s ∆ T , m is the mass, s is the specific heat and ∆ T is the temperature change. Case 1 : ∆ t = 2   minutes ,   T 0 = 22 ° C m s × 12 2 = - K 98 + 86 2 - 22 6 = - K m s 70         . . . 1 Case 2 : m s × 6 Δ t = - K 75 + 69 2 - 22 6 Δ t = - K m s ( 50 )       . . . 2 Dividing (2) by (1), we get ⇒ 6 Δ t ( 6 ) = 50 70 ⇒ &#916