Understanding the Time to Boil Dry a Kettle: A Detailed Analysis
Introduction
In this detailed analysis, we will explore the science behind how long it takes for a 3-kilowatt (3kw) kettle containing 1.5 kilograms of water to completely boil dry. We'll utilize key concepts such as heat capacity, latent heat of vaporisation, and power consumption to provide a thorough understanding of this process.
Key Concepts
Before diving into the calculations, let's clarify some fundamental concepts:
Heat Capacity: This is the amount of heat required to raise the temperature of a substance by one degree Celsius. For water, it is 4.2 kilojoules (kJ) per kilogram per degree Celsius (kg·°C). Latent Heat of Vaporisation: This is the amount of energy required to change a substance from a liquid to a gas without changing its temperature. For water, it is 2.23 megajoules (MJ) per kilogram (MJ/kg). Kettle Power Consumption: This refers to the rate at which the kettle consumes electrical energy. A 3-kilowatt (3kW) kettle consumes 3000 watts (W), meaning it supplies 3000 joules (J) of energy per second.The Problem: Boiling Dry a Kettle
The specific scenario we are addressing is: a 3-kilowatt kettle containing 1.5 kilograms of water is left switched on. We need to determine how long it will take for the kettle to boil all the water dry.
Calculations
To solve this problem, we need to calculate the total energy required to boil 1.5 kilograms of water to a gaseous state and then determine how long it will take to supply that energy with a 3-kilowatt kettle.
Step 1: Calculate the Latent Heat Required to Vaporise the Water
First, we need to calculate the energy required to vaporise 1.5 kilograms of water. The formula for this is:
Energy required for vaporisation mass of water × latent heat of vaporisation
Using the given values:
Energy required 1.5 kg × 2.23 MJ/kg 3.345 MJ
Converting mega joules to kilojoules:
Energy required 3.345 MJ 3,345,000 J
Step 2: Determine the Time to Supply This Energy
The kettle supplies 3000 joules of energy per second. To find out how long it will take to supply 3,345,000 joules, we divide the total energy required by the power supply rate:
Time Energy required / Power supply rate
Time 3,345,000 J / 3000 J/s 1115 seconds
Conclusion and Additional Insights
After starting the boiling process, it will take approximately 1115 seconds or about 18.58 minutes to completely boil dry all the water in the 3-kilowatt kettle containing 1.5 kg of water. This theoretical calculation can help in real-world applications such as understanding energy consumption in household appliances.