How long will a 1.2 kW electric kettle take to heat 0.8 kg of water from 20°C to 100°C?
A person decides to loose weight by eating only cold food. A 100 g piece of apple pie yields 1500 kJ of energy when eaten. It its specific heat is 1.7 kJ/kg °C, how much less energy is its energy component at 5°C than at 25°C?
3.687 min
To calculate the time it takes for the electric kettle to heat water from 20°C to 100°C, we can use the equation Q = mcΔT.
Q is the amount of heat energy required to heat the water, m is the mass of water, c is the specific heat capacity of water, and ΔT is the change in temperature.
1. First, we need to calculate the amount of heat energy required to heat the water:
Q = mcΔT
Q = (0.8 kg) × (4,186 J/kg°C) × (100°C - 20°C)
Q = (0.8 kg) × (4,186 J/kg°C) × (80°C)
Q = 268,288 J
2. Next, we need to calculate the power (P) of the electric kettle:
P = 1.2 kW
3. Finally, we can calculate the time (t) it takes to heat the water using the equation P = Q/t:
t = Q / P
t = 268,288 J / (1,200 W)
t = 223.57 seconds
t ≈ 3.73 minutes
Therefore, it will take approximately 3.73 minutes for the 1.2 kW electric kettle to heat 0.8 kg of water from 20°C to 100°C.
To find out how long the 1.2 kW electric kettle will take to heat 0.8 kg of water from 20°C to 100°C, we need to calculate the amount of heat required and then determine the time based on the kettle's power rating.
First, we need to find the amount of heat required to raise the temperature of the water from 20°C to 100°C. This can be done using the formula:
Q = mcΔT
Where:
Q is the heat energy (in Joules),
m is the mass of the water (in kg),
c is the specific heat capacity of water (approximately 4186 J/kg°C), and
ΔT is the change in temperature (in °C).
Substituting the given values:
m = 0.8 kg (mass of water)
c = 4186 J/kg°C (specific heat capacity of water)
ΔT = 100°C - 20°C = 80°C
Q = (0.8 kg)(4186 J/kg°C)(80°C)
Q = 267,008 J
Now, we know the amount of heat required is 267,008 Joules.
Next, we need to calculate the time it will take for the electric kettle to generate this amount of heat. The power rating of the kettle is given as 1.2 kW.
Power is defined as the rate at which work is done or energy is transferred, and it can be calculated using the formula:
Power = Energy / Time
Rearranging the formula, we can solve for time:
Time = Energy / Power
Substituting the values:
Energy = 267,008 J (amount of heat required)
Power = 1.2 kW (power rating of the electric kettle)
Time = (267,008 J) / (1.2 kW)
To convert kilowatts (kW) to watts (W), we need to multiply the power rating by 1000:
Time = (267,008 J) / (1.2 kW * 1000 W/kW)
Time = (267,008 J) / (1200 W)
Time ≈ 222.51 seconds
Therefore, it will take approximately 222.51 seconds (or about 3 minutes and 42 seconds) for the 1.2 kW electric kettle to heat 0.8 kg of water from 20°C to 100°C.