To prove that 1 kilopascal liter (kPa L) is equivalent to 1 joule (J), we need to understand the relationship between these units.
A kilopascal (kPa) is a unit of pressure, where 1 kPa is equal to 1000 pascals (Pa). The pascal is defined as one newton per square meter (N/m²). So, we have:
- 1 kPa = 1000 Pa = 1000 N/m²
Now, a liter (L) is a unit of volume, which is equal to 0.001 cubic meters (m³). So:
- 1 L = 0.001 m³
When we combine these conversions, we can express 1 kPa L in joules. The unit joule (J) is defined as one newton meter (N·m). Now, let’s compute:
Using the definitions above:
- 1 kPa L = 1 kPa × 1 L
- = 1000 Pa × 0.001 m³
- = 1000 N/m² × 0.001 m³
- = 1000 N × 0.001 m = 1 N·m
- = 1 J
Thus, we see that:
- 1 kPa L = 1 J
This shows, through mathematical proof, that one kilopascal liter is indeed equal to one joule.