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Notes by Category University Engineering

Mechanics & Stress Analysis*
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Properties of Substances

In order to predict how systems will behave, we need to understand their properties at different equilibrium states.

Pure Substances

A pure substance is one that is chemically homogenous (it has the same chemical composition everywhere in the substance). Examples include

  • hydrogen

  • pure water

  • a mixture of water and steam

  • air (all the gaseous substances are distributed evenly, everywhere)

Examples do not include

  • Mixtures of oil and water (oil is not soluble in water, so the two will always be separate)

  • Mixtures of liquid and gaseous air (different parts of air condense at different temperatures, so the mixture is not homogeneous)

Phase Changes

While there are three main phases a substance can be in (solid, liquid and gas), there are also a number of sub-phases within these:

As you can see, the liquid phase is broken into two bands:

  • subcooled (compressed) liquids are when the liquid is not about to evaporate. For example, water at 20°C

  • saturated liquids are when the liquid is about to evaporate. For example, water at 100°C

The gas phase is also split into two bands:

  • saturated vapours are vapours that are about to condense. This region overlaps with the saturated liquids phase, so at 100°C, water exists as a mixture of liquid about to vaporise and vapour about to liquify

  • superheated vapours are gases that are not about to condense. For example, steam at 300°C

The boiling point is also referred to as the saturation temperature and pressure. This is the given temperature and/or pressure that the liquid-vapour mixture is seen. It is important to note that the temperature remains constant during a phase change.

There are two other important point between phases: the critical and the triple point.

  • At the triple point, gas, solid and liquid phases can coexist.

  • Above the critical point, liquid and vapour can no longer be distinguished. It is the high-pressure form of the liquid-vapour mixture phase, known as the supercritical fluid phase.

Latent Heat

The energy absorbed or released during a phase change between solid and liquid is called latent heat of fusion; that absorbed or released between the liquid and vapour states is called latent heat of vaporisation.

Behaviour of Gasses

Equations of state (EoS) are laws that apply at any point in a given state. These are helpful to describe and model the behaviour of substances, especially of ideal gasses. Making three assumptions about gasses simplifies the models greatly:

  1. Momentum is conserved when gas molecules collide with the container wall

  2. Gas molecules have negligible volume

  3. Any attractive forces between gas molecules is negligible

These assumptions are known as the kinetic theory of gasses, and give us the ideal gas EoS:

A more common form of the equation uses the specific gas constant, R, and the mass, m, of gas:

Dividing both sides by the mass gives the specific volume form:

Since R is constant, we can write this as:

It follows from this that specific internal energy, u, is only a function of temperature, and not pressure:

When Kinetic Theory Doesn’t Apply

If we cannot assume that molecular volume and inter-molecular attraction are negligible, then the EoS has to be re-written in van der Waals form:

Perfect Gases

If the process occurs over a very small change in temperature, we can model the ideal gas EoS as being linear:

Cv here is the specific heat at a constant volume.