Question

The temperature of an object measures 90℉is taken outside where the temperature is 10℉. After 5 minutes, the temperature of the object measures 70℉. Find the temperature reading on the thermometer 30 minutes after having been outside.

Answer 1

I using Newton Law of cooling o let time is token in min, Temperature inf dT = -K (T-Ts) dt where Tis tem perature of body Is is temperature of Surrounding Ts = 10°F dT = -K (T-10) dt /dt = f-kat J T-50 ln (T-10) = -kt te (T-10) = A ekt T = gor at t=0 80 A (T-10) = 800 kt at t=5, T-70F 60 - 80 ekts) 3 = p X(5) so e-K(30) = 13410 To find T when t= 30 min (T-10) = 80 ek (30) (T-10 ) = 80 • (34)" so T = 24.238°F 80 Temperature after 30 min=24.238°F