Math Problem Statement

The diagram below shows three kettles with their powers and the time they take to boil 500 cm³ of water. How much energy is transferred (in kilojoules, kJ) by the 1.4 kW kettle while it boils the water?

Solution

To find the energy transferred by the 1.4 kW kettle during the time it takes to boil the water, we can use the formula:

Energy=Power×Time\text{Energy} = \text{Power} \times \text{Time}

Where:

  • Power is 1.4 kW (kilowatts),
  • Time is 4.5 minutes.

First, we need to convert time from minutes to seconds since power in kilowatts is in kilojoules per second.

4.5minutes=4.5×60=270seconds4.5 \, \text{minutes} = 4.5 \times 60 = 270 \, \text{seconds}

Now, calculate the energy transferred:

Energy=1.4kW×270seconds\text{Energy} = 1.4 \, \text{kW} \times 270 \, \text{seconds}

Energy=378kJ(kilojoules)\text{Energy} = 378 \, \text{kJ} \, (\text{kilojoules})

Thus, the energy transferred by the 1.4 kW kettle is 378 kJ.

Would you like further details or have any other questions?

Here are 5 related questions to deepen your understanding:

  1. How would the energy transfer change if the power of the kettle were higher?
  2. How is energy transfer affected by changing the volume of water to be heated?
  3. What units of measurement are commonly used to calculate energy in different scenarios?
  4. Why is time converted into seconds when calculating energy transfer?
  5. How can you reduce the time to boil water using the same kettle?

Tip: Always ensure that units of measurement are consistent when applying formulas for power, energy, and time!

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Math Problem Analysis

Mathematical Concepts

Energy Transfer
Power-Time Relationship
Unit Conversion

Formulas

Energy = Power × Time

Theorems

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Suitable Grade Level

Grades 9-11