A thermometer reading 10 degrees C is brought into a room with a constant temperature of 38 degrees Upper C. (a) If the thermometer reads 14 degrees C after 4 minutes, what will it read after being in the room for 6 minutes?

Explanation:

We shall apply Newton's laws of cooling .

dT / dt = k ( T₁ - T₂ )

dT is change in temperature in time dt , k is constant , T₁ and T₂ are temperature of cold  object and hot surrounding respectively.

For  the first case of 4 minutes

(14 - 10)/ 4 = k [(14+10) /2 - 38 ]  , T₁ = (14+10) /2 , the average  temperature

1 = - 26 k

Using the formula for next two minutes

T-14 / 2 = k [(14+T) /2 - 38 ]

T-14 / 2 = 1/26[ 38 - (14+T) /2 ]

T / 2 - 7 = 1.46 - .27 - T / 52

T/2 + T/52 = 7 + 1.46 - .27

= .52 T = 8.19

T = 15.75 degree