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Notes by Category University Engineering

Mechanics & Stress Analysis*
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Foundations of Thermodynamics

There are four Laws of Thermodynamics:

  1. The Zeroth Law of Thermodynamics says that if two bodies are in thermal equilibrium with a third body, the two bodies are also in thermal equilibrium with one another

  2. The First Law of Thermodynamics states that energy can neither be created nor destroyed: it always exists, and can only be converted from one form into another

  3. The Second Law of Thermodynamics

  4. The Third Law of Thermodynamics

The Macroscopic Viewpoint

We know that substances are made up of particles and molecules. For example, a gas exerts a pressure on its container due to the individual molecule collisions with each other and the walls. This is called classical thermodynamics, but this microscopic viewpoint is not particularly helpful for engineering problems as it overcomplicates things massively.

Instead, we model the particles grouped together as a substance. This is called the macroscopic viewpoint and it applies the continuum assumption that properties within a substance are equally and evenly distributed.

Systems and Control Volumes

Systems are defined as certain amounts of matter within a specified space. Everything outside the system is known as the surroundings, where the boundary is the zero-thickness line that separates the two. Boundaries can be fixed (such as a pressure vessel) or movable (a piston).

If no matter can cross the boundary, the system is said to be closed. Energy in both heat and work forms can cross the boundary, and the volume is not fixed.

If no matter nor energy can cross the boundary, the system is said to be isolated.

If both mass and energy can cross the boundary, the system is said to be open – or more commonly, it is described as a control volume. Examples include turbines or compressors: the volume is arbitrarily defined in space and is fixed, though the boundaries can move.

Properties of Systems

All systems have properties that are true anywhere in the system. These could be intensive of extensive:

  • Intensive properties are independent of a system’s size (e.g. temperature, pressure, and any constants such as viscosity)

  • Extensive properties are dependent on a system’s size (e.g. total mass and volume)

Specific properties are extensive properties per unit mass, and are noted using the lower-case version of their assigned letter:

  • V is the total (extensive) volume of the system

  • v is the specific volume, the volume per unit mass, V/m

The properties of a system in a given state do not depend on the circumstances by which the system came to be in that state.

Simple Compressible Systems

A ‘simple compressible system’ is one which can be fully defined by two independent intensive properties. This is when the impact of gravity, motion, and many other properties such as magnetic fields can be neglected.


If a system is in equilibrium, it is not experiencing any change. All the properties are uniform (do not vary in space) and steady (do not vary in time): they are said to be constant and describe the state of the system. As soon as one property changes, so does the state.

If a system is totally independent from its surroundings – there is no heat or work transfer across the system boundary – then the system is in internal equilibrium. Nothing from the surroundings can impact the properties of the system, and so there is no change in properties with respect to time.

Here, the gas is an insulated system in equilibrium:

If the diaphragm breaks, the system is no longer in internal equilibrium:

Eventually, a new internal equilibrium is reached, where the gas is at a lower pressure:

When a system is impacted by its surroundings, equilibrium is also reached. A common example is a movable piston: in its initial state, the piston is held in a fixed position and the gas (the system) is in compression, at a greater pressure than the surroundings:

Then, the peg is removed so piston can move, and so it moves until the forces from pressure on either side of the piston are balanced:

If the same system were arranged vertically, the weight of the piston would need to be considered as well. Problems like this are solved simply by resolving forces, remembering that:

Processes, Paths & Cycles

A process is when a system changes from one state to another. The path is the steps taken to complete that process – e.g. any intermediate states. Processes are defined in terms of the initial and final states, and the properties at each of these states:

If a process is particularly slow, and the change in state is infinitesimally small per unit time throughout, we can model the process as quasi-equilibrium (sometimes called quasi-static). This is because at every point throughout the process, the system may as well be in equilibrium: for example, a slow moving piston.

If the piston is suddenly stopped, and the ‘settling time’ for the system to return to equilibrium is miniscule (< 1/10th speed of sound) in comparison to the time taken to notice a change in properties, the process is described as quasi-equilibrium.