How long does it take a 1000. W electric kettle to bring 1.0L of water to the boiling point if the temperature of the water and the kettle is 15 C? The kettle os made of 0.400kg of iron. Assume that no water is lost to steam, and that the kettle is 100% efficient.

To find the time it takes for the electric kettle to bring 1.0L of water to the boiling point, we can use the concept of heat transfer.

Step 1: Calculate the heat required to raise the temperature of the water:
The specific heat capacity of water is 4.186 J/g°C.
The mass of 1.0L of water is 1000 g (since 1 mL of water = 1 g).
The initial temperature of the water is 15°C, and the boiling point of water is 100°C.
ΔQ = mcΔT
ΔQ = (1000 g)(4.186 J/g°C)(100°C - 15°C)
ΔQ = 417,100 J

Step 2: Calculate the time using the power of the electric kettle:
Power is given as 1000 W, which means it supplies 1000 J of energy every second (J/s).

Time = ΔQ / Power
Time = 417,100 J / 1000 J/s
Time = 417.1 s

Therefore, it would take approximately 417.1 seconds (or 6 minutes and 57 seconds) for the 1000 W electric kettle to bring 1.0L of water to the boiling point.

To determine how long it takes for the electric kettle to bring 1.0L of water to the boiling point, we need to consider the energy required to raise the temperature of the water and the kettle.

First, let's calculate the energy required to raise the temperature of the water from 15°C to 100°C. We can use the specific heat capacity of water, which is 4.186 J/g°C. Since we have 1.0L of water, which is equivalent to 1000g, the energy required can be calculated as:

Energy = mass * specific heat capacity * temperature change.
= 1000g * 4.186 J/g°C * (100°C - 15°C).
= 347,950 J.

Next, let's calculate the energy required to heat the kettle from 15°C to 100°C. We can use the specific heat capacity of iron, which is 0.450 J/g°C. Since the mass of the kettle is 0.400kg, the energy required can be calculated as:

Energy = mass * specific heat capacity * temperature change.
= 0.400kg * 0.450 J/g°C * (100°C - 15°C).
= 14,850 J.

Now, let's calculate the total energy required:

Total energy = energy required for water + energy required for kettle.
= 347,950 J + 14,850 J.
= 362,800 J.

Considering that the kettle is 100% efficient, all the electric power of 1000 W will be converted into heat. The relationship between power, energy, and time is:

Energy = power * time.

Rearranging the equation to solve for time:

Time = Energy / Power.
= 362,800 J / 1000 W.
= 362.8 seconds.

Hence, it will take approximately 362.8 seconds, or 6 minutes and 2.8 seconds, for the electric kettle to bring 1.0L of water to the boiling point.