Question

Newton’s law of cooling relates the temperature, T, of an object at time t in an environment with constant

temperature T0 by the equation where k is a constant.

kT0 = dT/dt + kT dt

1. a) Show that T = Ae−kt + T0 satisfies the above equation.

2. b) A dead body with temperature T = 28 degrees is found in a room where the temperature T0 = 20 degrees. Assuming that the body was initially at a temperature A = 37 degrees, and that k = 2 hr−1 estimate how long the body has been in the room.

Answer 1

k To k kT --k(T-T.) T-T nT-To Am A -kt) T-To kt 1 A - kt T- To A e A e + To -proned k= 2 hr i linon A = 3¥° To 20 28 28 3Y 2t 2 0 2t 3e eat 34 2 f