Question

This exercise uses Newton's Law of Cooling. A roasted turkey is taken from an oven when its temperature has reached 185°F and is placed on a table in a room where the temperature is 76°F.
(a) If the temperature of the turkey is 145°F after half an hour, what is its temperature after 45 min? (Round your answer to the nearest whole number.)
(b) After how many hours will the turkey cool to 100°F? (Round your answer to one decimal place.)

Answer 1

Newton la o Coeling dT -k T- To de Oven at ah time T T- Tempretro f To -Roon Tempreture , k- Constand Integrate i euation 'oT - kdt T-To) k tt C Ln T-To) To T6 F * t omin, T- 186F t 30 min, T= 148F Put inGieuahon t-0 min, TE 105F ln C18s-76) С -

30 min T- 14s F Ln Liu5-76) k x 30 Rn lo9 +O.4S7 +k 30 T ? 45 min Ln CT-76)-ki tc - o us7 n 109 x ys 30 n T-76 109 o 6855 T-76 O SO38 109 130.91F

(b) 2 T 100F t - Kt tC Rn (loo-76) xt t n10q 30 O.4S7 -1.S13 11 3 0 t 99-34 min 1. 6S hous