Question

A body cools from 60°C to 50°C in 10 minutes and 50° to 40°C in the next 15 minutes. The room temperature is?
Please answer fast.. Its urgent ​

Answer 1

Explanation:

According newton's law of cooling,

                   T=Ts+(To−Ts)e−kt

        where, T= temp. at any time t

                    To=initial temp.

                   Ts=surrounding temp.

                    t=time

                    k=cooling constant

since body cools initially from 60℃ to 50℃in 10 min.

so from above equation,

                      50=20+(60-20)e−k(10)

                    ⇒43=e−10k        eqution(1)

we need to find the temp. at the end of next 10 min. i.e. 20 min. from start

so again using newton's law of cooling formula,

                      T=Ts+(To−Ts)e−kt

                   ⇒T=20+(60-20)e−k(20)

                    ⇒T=20+(40){e−10k}2     equation (2)

from equation (1) and (2), we get

                    ⇒T=20+(40)(43)2

                    ⇒T=42.5 ℃