Sunday, March 8, 2015

How long to boil 1 Liter of water in 1500 watts kettle

Solution:

Cp = 4.19 KJ/(kg·C)
This is the specific heat of water at 15 °C and 101.325 kPa atmospheric pressure.
This is the amount of energy required to raise the temperature of  1 kg  ( 1 Liter )  of water by 1 °C.

Density of water:

1 kg/Liter
1000 kg/cubic meter
1 metric ton/cubic meter
1 g/cubic centimeter
1 g/ml


Boiling water for coffee/tea:

1 Liter is approximately 4 cups (good for a family of four)
100 °C is the boiling point of water at a pressure of 1 atm (101.325 kPa)


Temperature of cold tap water and hot water:

cold tap water is around 15 °C
in most homes, hot water heaters are set at 60 °C (140 °F)


Heat Calculation Formula:


Q = m x Cp x (T2-T1)

where:
Q = heat energy required to boil water, KJ
m = mass of water, kg
Cp = specific heat of water, 4.19 KJ/(kg·C)
T2 = boiling point of water, 100 C
T1 = temperature of cold tap water, 15 C

Q = 1 kg x 4.19 KJ/(kg·C) x (100 C - 15 C)

Q = 357 KJ


Black and Decker Kettle Power Rating:

1500 watts heating power
1500 watts is equal to 1.5 KW (KJ/sec)



Time to boil 1 Liter (1 kg) of water from 15 C:


assuming no heat is lost,

time = Q/Power of kettle

time = 357 KJ/1.5 KJ per second

time = 238 seconds

time = 4 minutes


Note: under the same conditions,

a. boiling 2 Liters of water would double the time to boil --> 8 minutes
b. using twice the kettle power (3000 watts) requires only half the boiling time --> 2 minutes

 
Time to raise 1 Liter of water 1 degree Celsius


using the same 1500-watt kettle, and assuming no heat loss

Q = 1 kg x 4.19 KJ/(kg·C) x (1 C)

Q = 4.19 KJ


time = 4.19 KJ/1.5 KJ per second

time = 3 sec


Note:

The time required to raise the temperature of water 1 degree C is dependent on,
a. amount (mass) of water
b. power rating of kettle

1 comment:

  1. your missing the energy required to make the phase change. this only gets the water to 100 liquid...

    ReplyDelete