Density Conversion Guide Converting 13.6 G/cm³ To Kg/m³

Density, a fundamental property of matter, is defined as mass per unit volume. It's a crucial concept in various scientific and engineering fields, including physics, chemistry, materials science, and fluid mechanics. Expressing density in different units is often necessary for calculations and comparisons. This article provides a detailed, step-by-step guide on how to convert the density of mercury, given as 13.6 grams per cubic centimeter (g/cm³), to kilograms per cubic meter (kg/m³). This conversion is not just a mathematical exercise; it's a practical skill that helps in understanding and applying scientific concepts effectively.

Understanding Density and Its Units

Before diving into the conversion process, let's clarify the concept of density and the units involved. Density is a measure of how much mass is contained in a given volume. The formula for density (ρ) is:

$\rho = \frac{m}{V}$

where:

• ρ (rho) is the density,
• m is the mass,
• V is the volume.

The most common units for density are grams per cubic centimeter (g/cm³) and kilograms per cubic meter (kg/m³). The unit g/cm³ is frequently used in chemistry and materials science due to its convenience for laboratory-scale measurements. On the other hand, kg/m³ is the standard SI (International System of Units) unit for density, widely used in physics and engineering applications. Understanding these units and their relationships is crucial for accurate conversions and calculations.

Step-by-Step Conversion of 13.6 g/cm³ to kg/m³

The given density of mercury is 13.6 g/cm³. To convert this to kg/m³, we need to convert grams to kilograms and cubic centimeters to cubic meters. Here's the detailed process:

Step 1: Convert Grams (g) to Kilograms (kg)

We know that 1 kilogram (kg) is equal to 1000 grams (g). Therefore, to convert grams to kilograms, we divide the number of grams by 1000.

• Conversion factor: 1 kg = 1000 g

So, to convert 13.6 g to kg, we perform the following calculation:

$\frac{13.6 \text{ g}}{1} \times \frac{1 \text{ kg}}{1000 \text{ g}} = 0.0136 \text{ kg}$

Thus, 13.6 grams is equal to 0.0136 kilograms. This conversion is a fundamental step, ensuring that we are working with the correct mass unit in our final calculation. The simplicity of this conversion belies its importance in the overall process.

Step 2: Convert Cubic Centimeters (cm³) to Cubic Meters (m³)

Next, we need to convert the volume unit from cubic centimeters to cubic meters. We know that 1 meter (m) is equal to 100 centimeters (cm). Therefore, 1 cubic meter (m³) is equal to $(100 \text{ cm})^3 = 1,000,000 \text{ cm}^3$.

• Conversion factor: 1 m³ = 1,000,000 cm³

To convert cubic centimeters to cubic meters, we divide the number of cubic centimeters by 1,000,000. In our case, we are starting with a density expressed per cubic centimeter, so we are effectively converting the