Question

Inside the hot room the thermometer reading is t_0f. The thermometer is taken outside where the ambient temperature is 5 f. After 1 minute the thermometer reads 55 f, and after 5 minutes the reading is 30 f. Determine the temperature t_0f of the room.

Answer 1

is required to find the initial temperature of the inside room using the given conditions.

Suppose that a thermometer shows the initial temperature of the inside room is

Now the thermometer taken from inside room to the out-side room where the air temperature is. That is,

Let be the temperature of the in-side room at time .

After 1 minute, the thermometer at reads. That is,

After 5 minutes, the thermometer at reads. That is,

Use these details in the differential equation suitable to Newton’s law of cooling,