A body cools in 7 minutes from 60^ C to 40^ C. What time (in minutes) does it take to cool from 40^ C to 28^ C, if its surrounding temperature is 10^ C ? (Newton's law of cooling holds good)

Step-by-step solution

Using Newton's law of cooling: ( T₁ - T₀ T₂ - T₀ ) = kt For the first interval, the body cools from 60^ C to 40^ C in 7 minutes with surrounding temperature T₀ = 10^ C: ( 60 - 10 40 - 10 ) = k(7) ( 50 30 ) = 7k ( 5 3 ) = 7k For the second interval, the body cools from 40^ C to 28^ C in time t : ( 40 - 10 28 - 10 ) = kt ( 30 18 ) = kt ( 5 3 ) = kt Comparing the two equations, we get: kt = 7k t = 7 minutes. Answer: 7