This accuracy and assumption optimization must be made by engineers, which is also called an engineering approach.
To start adopting the engineering approach stated above, you need to know the intensive and extensive properties of a system.
What Are the Extensive Properties?
To make engineering calculations and assumptions, you need to know the ‘properties’ of the system that you are dealing. ‘Properties’ of a system are all the characteristics that affect the calculations and results that you are making.
The extensive properties of a system are the property that depends on the size and amount of matter in that system. For example, the total mass of the system is an extensive property of a system. It depends on the amount of matter and the size of the system. Also, the total momentum(M) of a system depends on the velocity and mass of the system.
Intensive Properties?
As you understand from the extensive properties, the intensive properties of a system are not dependent on the mass or size of the system. For example, the density(ρ) of an object. The density of a system does not change with the changing amount and size. It’s all same.
But there is another type of property that is generally used in engineering calculations.
Specific Properties of Systems
Specific properties of systems are the extensive properties that are divided by the total mass or volume. For example, the specific total energy is calculated by the division of total energy(E) with the mass(m)
If you notice that, extensive properties of systems are denoted by the uppercase letter such as energy(E), and the intensive and specific properties of systems are denoted by the lowercase letters such as density(ρ).
Continuum in Engineering
Continuum is a very important approach and assumption in engineering calculations. In continuum assumption, the mass or the matter of the system is considered to be homogenous in all directions. All the properties are the same in all directions. The slight differences around the mass because of the molecular effects are neglected in calculations. With this assumption, calculations are much easier.
It depends on the activities of molecules in a system. If the molecular activities such as movement and vibrations of molecules are drastically small according to the system to be analyzed, continuum assumptions can be used.
Think about you are dealing with 100 kg of water as a system. In this amount of water, there are trillions of water molecules, and the vibration and movement ranges of these molecules are very small compared to the whole 100kg of the water system. So, continuum assumptions and approaches can be adopted in engineering calculations.
Let’s give an example where a continuum can not be adopted. In an extensively vacuumed system where the number of molecules is scarce, movements and vibrations of these low amounts of molecules are very high. This means the continuum assumption can not be applied.
Conclusion
The logic of the extensive and intensive properties of materials and engineering systems can be summarized as above. Continuum mechanics are derived from the fundamental information stated above.
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