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Show that 1kW-hr is the same as 3.6MJ

Show that 1kW-hr is the same as 3.6MJ

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Conversion of Energy Units: Kilowatt-Hour to Megajoules** **Problem Statement:** Show that 1 kilowatt-hour (kW-hr) is the same as 3.6 megajoules (MJ). **Solution:** To solve this problem, we need to understand the relationship between the units of energy: kilowatt-hours and megajoules. 1. **Understanding Kilowatt-Hour (kW-hr):** - A kilowatt-hour is a unit of energy that represents the amount of energy consumed by a power of 1 kilowatt over the period of one hour. - 1 kilowatt = 1000 watts 2. **Understanding Megajoules (MJ):** - A megajoule is a unit of energy in the International System of Units (SI), where 1 megajoule = 1,000,000 joules. 3. **Conversion Steps:** - First, convert the kilowatt-hour into watt-seconds (joules): ``` 1 kW-hr = 1 kW × 1 hr = 1000 watts × 3600 seconds (since 1 hour = 3600 seconds) = 3,600,000 watt-seconds (joules) ``` - Next, convert joules to megajoules: ``` 3,600,000 J = 3.6 MJ (since 1 MJ = 1,000,000 J) ``` Therefore, we have shown that: 1 kilowatt-hour (kW-hr) = 3.6 megajoules (MJ).
Transcribed Image Text:**Conversion of Energy Units: Kilowatt-Hour to Megajoules** **Problem Statement:** Show that 1 kilowatt-hour (kW-hr) is the same as 3.6 megajoules (MJ). **Solution:** To solve this problem, we need to understand the relationship between the units of energy: kilowatt-hours and megajoules. 1. **Understanding Kilowatt-Hour (kW-hr):** - A kilowatt-hour is a unit of energy that represents the amount of energy consumed by a power of 1 kilowatt over the period of one hour. - 1 kilowatt = 1000 watts 2. **Understanding Megajoules (MJ):** - A megajoule is a unit of energy in the International System of Units (SI), where 1 megajoule = 1,000,000 joules. 3. **Conversion Steps:** - First, convert the kilowatt-hour into watt-seconds (joules): ``` 1 kW-hr = 1 kW × 1 hr = 1000 watts × 3600 seconds (since 1 hour = 3600 seconds) = 3,600,000 watt-seconds (joules) ``` - Next, convert joules to megajoules: ``` 3,600,000 J = 3.6 MJ (since 1 MJ = 1,000,000 J) ``` Therefore, we have shown that: 1 kilowatt-hour (kW-hr) = 3.6 megajoules (MJ).
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