Question

1 (15 poie) Acconding so Newson's law of ceeling if n obiect t sonee Ta innonel in a medm having the comstat smpeae M. then the ate of chnge of Ts ppol to the derece of temperatre M T This gives the dfferentil ouution M-T dr (a) Solve the diferential eqtion for 7 (b) A thermometer reading 100 F is placed in a medium having a comstant tmpee of 70'F. Ater 6 min the thermometer reads 80F. What is the reading after 20 min

Answer 1

= ( - T) – q To a. . solve the given differential equarian : EK CM-T) I kdr on Which gives integrarion, Koh - MrT Log being inreghesabze Comment 1 akt -log (M-T) + loge zur log ( 7 ) Fickr - M-T= cekr - T = M- cean -KE Am. - by the given problem, T (0) = 100% T(6)=80°F M . 70°F To fine, T (20) = ? from -* 100. 70-e s es -30 264 80- 70 +30 e 6 2 Bol = 10

:-64 ni > -6K = log Cate 5) Ka 0:183 T (20) = 70 +30 e 20% 5 70.77 am After 20 min reading will be 70.77°F. -20% 0.183 n .: 77°F Ayo