Calculating Boiling Time for Water with a 100W Kettle

Successfully boiling water using a kettle is a common task, but understanding the underlying physics and mathematics can be quite enlightening. In this article, we will explore the process of boiling 0.25 kg of water at a specific temperature using a 100W kettle rated at 240V in an environment where the operating voltage is 220V. Let's delve into the calculation and learn how long it will take for the water to boil.

Given Data and Assumptions

To determine the boiling time, we need to consider the following data and assumptions:

Power of kettle: 100 watts (adjusted for 220V) Voltage rating of the kettle: 240V Operating voltage: 220V Mass of water: 0.25 kg Specific heat capacity of water: 4184 J/kg·K Heat capacity of kettle: 400 J/K Initial temperature of water: 20°C Final temperature of water (boiling point): 100°C

Calculation Steps

Calculate the heat required to raise the temperature of the water: Calculate the heat required to raise the temperature of the kettle: Total heat required: Adjust the power of the kettle for the operating voltage: Calculate the time required to supply the total heat:

Step-by-Step Calculation

1. Calculate the heat required to raise the temperature of the water:

[ Q_{text{water}} m_{text{water}} cdot c_{text{water}} cdot (T_{text{final}} - T_{text{initial}}) ]

[ Q_{text{water}} 0.25 text{kg} cdot 4184 text{J/kg·K} cdot (100 - 20) text{K} ] [ Q_{text{water}} 20920 text{J} ]

2. Calculate the heat required to raise the temperature of the kettle:

[ Q_{text{kettle}} C_{text{kettle}} cdot (T_{text{final}} - T_{text{initial}}) ]

[ Q_{text{kettle}} 400 text{J/K} cdot (100 - 20) text{K} ]

[ Q_{text{kettle}} 32000 text{J} ]

3. Total heat required:

[ Q_{text{total}} Q_{text{water}} Q_{text{kettle}} ] [ Q_{text{total}} 20920 text{J} 32000 text{J} 52920 text{J} ]

4. Adjust the power of the kettle for the operating voltage:

[ P_{text{effective}} P cdot left( frac{V_{text{operating}}}{V} right)^2 ]

[ P_{text{effective}} 100 text{W} cdot left( frac{220}{240} right)^2 ]

[ P_{text{effective}} 100 text{W} cdot left( frac{48400}{57600} right) approx 84.72 text{W} ]

5. Calculate the time required to supply the total heat:

[ t frac{Q_{text{total}}}{P_{text{effective}}} ]

[ t frac{52920 text{J}}{84.72 text{W}} approx 624.15 text{s} ]

Conclusion: It will take approximately 624.15 seconds, or about 10.4 minutes, for the water to reach its boiling point of 100°C.

Understanding and solving this problem using the principle of heat transfer can be crucial for improving the efficiency of household appliances and making informed decisions in daily life. This detailed calculation reveals the complexities of thermal energy and provides insight into practical applications of physics in everyday scenarios.