Question

Dr. McCord wants to make some tea, so she puts 450 g of water in a 250 g aluminum electric tea kettle that contains a 1000 W heating coil. The initial temperature of the water and kettle is 35°C. The specific heat of aluminum is 0.9 J/g-K and the specific heat of water is 4.186 J/g-K.

How long will it take to heat the water until it begins boiling?

Answer 1

Step 1: Find amount of energy required to raise temperature of water + kettle to boiling point of water

Q = Q1 + Q2

Q1 = Energy required to raise temperature of water from 35 C to 100 C = Mw*Cw*dT

Q2 = Energy required to raise temperature of kettle from 35 C to 100 C = Mk*Ck*dT

So,

Q = Mw*Cw*dT + Mk*Ck*dT

Using given values: Mw = 450 gm = 0.45 kg, Mk = 250 gm = 0.25 kg

Cw = 4186 J/kg-K, Ck = 900 J/kg-K (Convert unit to kg)

Q = 0.45*4186*(100 - 35) + 0.25*900*(100 - 35)

Q = 137065.5 J

Step 2: Now relation between power and energy is given by:

Power = Energy/time required

P = Q/t

t = Q/P

P = Power of heating coil = 1000 W

So,

t = 137065.5/1000

t = 137.065 sec = 137.065/60

t = 2.28 min = time required (Use units as mentioned in question 137 sec OR 2.28 min)

Let me know if you've any query.