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Density is a fundamental concept in thermodynamics that tells us how much mass is contained in a given volume. It is usually represented by the Greek letter \( \rho \) and is calculated using the formula:
\[ \rho = \frac{m}{V} \]where:

• \( m \) is the mass.
• \( V \) is the volume.

For example, in the given problem, the density of granite is \( 2400 \text{ kg/m}^3 \). This means that every cubic meter of granite contains \( 2400 \text{ kg} \) of mass. Similarly, the air has a density of \( 1.15 \text{ kg/m}^3 \), indicating it is much less dense compared to granite. Understanding density helps us determine how substances are packed together within a given space, which is crucial when calculating volume and mass.

Specific volume is another key concept in thermodynamics. It is essentially the inverse of density and is defined as the volume occupied by a unit mass of a substance. The formula for specific volume is:
\[ v = \frac{V}{m} \]where:

• \( V \) is the total volume.
• \( m \) is the total mass.

In the problem, the overall specific volume of the mixture in the container is determined. By finding the specific volume, \( v \approx 0.0055 \text{ m}^3/\text{kg} \), we understand that each kilogram of the combined mixture (granite and air) takes up about \( 0.0055 \text{ m}^3 \) of space. Knowing specific volume allows us to analyze the compactness of different materials when mixed, which is particularly useful in engineering and material science.

Mass calculation is crucial in both understanding and manipulating the properties of different substances. In thermodynamics, knowing the mass allows us to figure out how much matter we have. To calculate mass, you often use the formula:
\[ m = \rho \times V \]where:

• \( \rho \) is the density.
• \( V \) is the volume.

In the exercise, after determining the available volume for air, we find its mass by multiplying its density \( (1.15 \text{ kg/m}^3) \) with the volume of air \( (4.625 \text{ m}^3) \), resulting in approximately \( 5.32 \text{ kg} \). Mass calculation is fundamental in determining how much of a material is present within a particular space, and it guides us in applications ranging from everyday recipes to industrial processes.

Volume calculation helps us determine how much space a certain amount of mass takes up, which is crucial in many practical applications. The relationship between mass, volume, and density can be expressed as:
\[ V = \frac{m}{\rho} \]where:

• \( m \) is the mass.
• \( \rho \) is the density.

In the problem, the volume of the granite is found by dividing its mass \( (900 \text{ kg}) \) by its density \( (2400 \text{ kg/m}^3) \), giving \( 0.375 \text{ m}^3 \). Volume calculation is essential not just in storing substances but also in ensuring that containers are appropriately designed for specific materials. Understanding volume helps us efficiently manage space in both everyday and specialized contexts.