An electric kettle contains 1.5 kg of water at
100o
C and powered by a 2.0 kW electric element. If the thermostat of the kettle fails to operate, approximately how long will it take for the kettle boil dry? (Take the specific latent heat of vaporization of water as
2000kJkg−1)
Answer
To determine how long it will take for the kettle to boil dry, we can calculate the amount of heat energy required to completely evaporate the water.
Step 1: Calculate the heat energy required to raise the temperature of the water from 100°C to its boiling point.
The specific heat capacity of water is 4.18 kJ/kg°C.
Heat energy = mass × specific heat capacity × temperature change
= 1.5 kg × 4.18 kJ/kg°C × (100°C - 100°C)
= 0 kJ
Step 2: Calculate the heat energy required to convert the water at its boiling point to steam.
The specific latent heat of vaporization of water is 2000 kJ/kg.
Heat energy = mass × specific latent heat of vaporization
= 1.5 kg × 2000 kJ/kg
= 3000 kJ
Step 3: Calculate the total heat energy required.
Total heat energy = Heat energy for temperature change + Heat energy for phase change
= 0 kJ + 3000 kJ
= 3000 kJ
Step 4: Calculate the time required.
Power is defined as the rate of energy transfer. Therefore, we can use the equation:
Power = Energy / Time
Rearranging the equation to solve for time:
Time = Energy / Power
= 3000 kJ / 2.0 kW
= 1500 seconds
Therefore, it will take approximately 1500 seconds (or 25 minutes) for the kettle to boil dry if the thermostat fails to operate.
To find out how long it will take for the kettle to boil dry, we need to calculate the time it takes for all the water to evaporate. The energy required to completely evaporate the water can be calculated using the specific latent heat of vaporization.
The equation we'll use is:
Energy = mass x specific latent heat of vaporization
First, let's calculate the energy required:
Energy = 1.5 kg x 2000 kJ/kg
Energy = 3000 kJ
Next, we need to calculate the power of the electric element:
Power = 2.0 kW
Now, we can use the formula for power to find the time it takes for the energy to be supplied:
Time = Energy / Power
Time = 3000 kJ / 2.0 kW
To make these units compatible, let's convert kJ to J and kW to W:
Time = 3000 kJ x 1000 J/kJ / 2.0 kW x 1000 W/kW
Time = 3000000 J / 2000 W
Time = 1500 s
Therefore, it will take approximately 1500 seconds for the kettle to boil dry if the thermostat fails to operate.
Q = rm= 2•10⁶•1.5=3•10⁶ J
t=Q/P= 3•10⁶/2•10³=1500 s=25 min=0.42 h