Convert between energy units. a. 534 kWh to J b. 215 kJ to Cal c. 567 Cal to J d. 2.85 × 10³ J to cal

Verified step by step guidance

1. Step 1: Understand the conversion factors needed for each part of the problem. For energy conversions, remember: 1 kWh = 3.6 × 10^6 J, 1 Cal = 4.184 kJ, and 1 cal = 4.184 J.
2. Step 2: For part a, convert 534 kWh to joules (J) using the conversion factor 1 kWh = 3.6 × 10^6 J. Multiply 534 kWh by 3.6 × 10^6 J/kWh.
3. Step 3: For part b, convert 215 kJ to Calories (Cal) using the conversion factor 1 Cal = 4.184 kJ. Divide 215 kJ by 4.184 kJ/Cal.
4. Step 4: For part c, convert 567 Cal to joules (J) using the conversion factor 1 Cal = 4.184 kJ. First, convert Calories to kilojoules by multiplying 567 Cal by 4.184 kJ/Cal, then convert kJ to J by multiplying by 1000 J/kJ.
5. Step 5: For part d, convert 2.85 × 10^3 J to calories (cal) using the conversion factor 1 cal = 4.184 J. Divide 2.85 × 10^3 J by 4.184 J/cal.

Key Concepts

Energy Units

Energy can be measured in various units, including joules (J), kilowatt-hours (kWh), kilojoules (kJ), and calories (Cal). Understanding these units is essential for converting energy values, as each unit represents a different scale of energy measurement. For instance, 1 kWh is equivalent to 3.6 million joules, while 1 Cal is approximately 4.184 joules.

Conversion Factors

Conversion factors are numerical values used to convert one unit of measurement to another. For energy conversions, specific factors are used, such as 1 kWh = 3.6 × 10^6 J, 1 kJ = 239.006 Cal, and 1 Cal = 4.184 J. Knowing these factors allows for accurate conversions between different energy units.

Dimensional Analysis

Dimensional analysis is a mathematical technique used to convert units by multiplying by conversion factors. This method ensures that units cancel appropriately, leading to the desired unit in the final answer. It is a systematic approach that helps verify the correctness of conversions and calculations in energy unit problems.