A thermometer is taken from a room where the temperature is 25oC to the outdoors, where the temperature is 3oC. After one minute the thermometer reads 14oC.

Question

A thermometer is taken from a room where the temperature is 25oC to the outdoors, where the temperature is 3oC. After one minute the thermometer reads 14oC.

(a) What will the reading on the thermometer be after 3 more minutes?

(b) When will the thermometer read 4oC? (minutes after it was taken to the outdoors. )

Answer 1

Use Newton's law of cooling dT/dt=k(T-Tenv) which is an ODE with solution T(t)=Tenv+(T(t)-Tenv)e^-t/τ .

Let Tenv = 3 and T(0)=25 and T(1)=14 ... solve to find τ=.693. Now, let find T(4) finding it = 3.069 degrees. Now let T=4 degree and solve for t = 2.14 minutes