Energy Conversion: 1000 K cal to kJ

This question requires converting a value from kilocalories (K cal) to kilojoules (kJ).

Understanding the Conversion Factor

The standard conversion factor between calories and joules is fundamental in physics and chemistry. Specifically:

• 1 calorie (cal) = 4.184 joules (J)
• Therefore, 1 kilocalorie (kcal) = 4.184 kilojoules (kJ)

Calculating 1000 K cal in kJ

To find the equivalent of 1000 K cal in kilojoules, we multiply the value in K cal by the conversion factor:

$1000 \text{ K cal} \times 4.184 \frac{\text{kJ}}{\text{K cal}}$

Performing the multiplication:

$1000 \times 4.184 = 4184 \text{ kJ}$

Thus, 1000 K cal is equal to 4184 kJ.

Final Answer Check

Comparing the calculated value with the options:

• Option 1: 4.184 kj - Incorrect
• Option 2: 4184 kj - Correct
• Option 3: 4.184 mj (megajoules) - Incorrect
• Option 4: 41.84 kj - Incorrect

The calculation confirms that 1000 K cal is equal to 4184 kJ.