The density of liquid nitrogen is 0.808 g/cm3 with a boiling point (-196 degrees Celsius/ 77K). Convert the density to units of kg/m3.
The Correct Answer and Explanation is:
Correct Answer:
The density of liquid nitrogen in kg/m³ is 808 kg/m³.
Step-by-step Conversion:
You are given the density of liquid nitrogen as: 0.808 g/cm30.808 \ \text{g/cm}^30.808 g/cm3
To convert to kg/m³, we use the following conversion factors:
- 1 g=0.001 kg1 \ \text{g} = 0.001 \ \text{kg}1 g=0.001 kg
- 1 cm3=1×10−6 m31 \ \text{cm}^3 = 1 \times 10^{-6} \ \text{m}^31 cm3=1×10−6 m3
Density=0.808 gcm3×0.001 kg1 g×106 cm31 m3\text{Density} = 0.808 \ \frac{\text{g}}{\text{cm}^3} \times \frac{0.001 \ \text{kg}}{1 \ \text{g}} \times \frac{10^6 \ \text{cm}^3}{1 \ \text{m}^3}Density=0.808 cm3g×1 g0.001 kg×1 m3106 cm3 =0.808×0.001×106 kgm3= 0.808 \times 0.001 \times 10^6 \ \frac{\text{kg}}{\text{m}^3}=0.808×0.001×106 m3kg =808 kgm3= 808 \ \frac{\text{kg}}{\text{m}^3}=808 m3kg
Explanation
Density is a fundamental physical property defined as mass per unit volume. In this problem, we are converting the density of liquid nitrogen from grams per cubic centimeter (g/cm³) to kilograms per cubic meter (kg/m³). These units are commonly used in different scientific contexts: g/cm³ is often used in chemistry or materials science for small-scale substances, while kg/m³ is standard in physics and engineering.
To convert, it’s important to realize how the units scale:
- 1 gram is 0.0010.0010.001 kilograms (since there are 1000 grams in a kilogram).
- 1 cubic centimeter is 1×10−61 \times 10^{-6}1×10−6 cubic meters (because 1003=1,000,000100^3 = 1,000,0001003=1,000,000 cm³ in 1 m³).
So, converting from g/cm³ to kg/m³ involves multiplying by 1000, which is the combined result of the mass and volume conversions: 0.808 g/cm3=0.808×1000=808 kg/m30.808 \ \text{g/cm}^3 = 0.808 \times 1000 = 808 \ \text{kg/m}^30.808 g/cm3=0.808×1000=808 kg/m3
This value tells us how much 1 cubic meter of liquid nitrogen weighs in kilograms. Knowing the density is critical in applications like cryogenics and fluid mechanics, especially since liquid nitrogen is used in cooling systems, medical storage, and scientific experiments. Its low boiling point of -196°C (or 77 K) highlights its cryogenic nature—it readily vaporizes at room temperature, and precise knowledge of its density helps ensure safety and effectiveness in its storage and use
