Boiling water at 1000 C is placed in a room which has a temp

Boiling water at 100⁰ C is placed in a room which has a temperature of 30⁰ C. It takes 15 minutes for the water to reach a temperature of 70⁰ C. When will the water temperature be at 40⁰ C?

Solution

Given that

Intially tempreture of water T(0) = 1000 C and room tempreture Ta = 300 C

It takes 15min for water to reach tempreture of 700 C .

T(15) = 700 ( tempreture of water after 15 min)

Newton\'s law of cooling

T(t) = Ta +(To-Ta) e^(-kt)

T(15) = 300 + ( 1000-300) e^(-15k)

700 = 300 + 700e^(-15k)

e^(-15k) = 4/7

-15k = -0.56

k= 0.037

hence tempreture time at which tempreture of water equal to 400

400 = 300 + (1000-300)e^(-kt)

e^(-kt) = 1/7

- 0.037t = -1.945

t = 52.59 min

after 52.59 it will be 400 C

answer