Thermodynamics and Engines

Thermodynamics, which deals with how work and energy (heat) are produced and consumed, is used to model engines. Thermodynamics allows us to ignore the complexities of the mechanical system and concentrate on the engine's input and output instead. The laws of thermodynamics determine the maximum efficiency of a heat engine and how work and energy are related.

At this point, it is important to talk about systems, which in physics can mean an object, a machine, or a living being. A system is anything that can take inputs and respond with outputs. A system's complexity can vary from an ice cube melting in water to a combustion engine or a power plant. Systems can be living beings or non-living objects; they can be as small as gas particles mixing in a room or as large as a planet and all its energy processes.

Thermodynamic systems

Anything can be a thermodynamic system, from the human body to the sun. Thermodynamic systems are useful to analyze energy and mass exchanges, without taking into account the details of all processes.

Thermodynamics and Engines: Heat

Heat is the thermal energy transferred to a system or an object. Heat energy exchange is usually described as a thermal change. The change of thermal energy is related to the kinetic energy of the particles that compose substances. The increase in kinetic energy is easily observed in liquids and gases.

Figure 1. Heat is the kinetic energy of the particles composing an object or substance. The particles on the left (T1) have more kinetic energy and, therefore, a higher temperature, Camacho - StudySmarter Originals

Thermal energy and the internal energy of a gas

The thermal energy of an object is the energy of its molecules or atoms. Thermal energy is the kinetic energy of its particles moving randomly. Higher the kinetic energy, the higher the thermal energy of the object.

The potential energy is the energy stored in the gas molecules. It is composed of the kinetic energy of the gas individual molecules and disordered movement, as also the potential energy between the molecules that compose it and uses the symbol "U".

The kinetic and potential energy should not be confused with the kinetic and potential energy of the gas as a whole.

Thermodynamics and Engines: Laws of thermodynamics

Thermodynamics has several important laws that describe how a system behaves when work, heat, and entropy change. These laws are universal, and every object in the universe follows them. There are four laws of thermodynamics:

• The zeroth law: the law of thermal equilibrium.
• The first law: the law that describes the internal energy of a substance.
• The second law: the entropy law of irreversibility.
• The third law: the law that states that at zero kelvin, entropy reaches a constant value.

The zeroth law of thermodynamics

The zeroth law of thermodynamics says that 'two objects or systems are in thermal equilibrium (at the same temperature) if both are in equilibrium with a third object or system'.

For example, when you remove two cupcakes from the oven, taking one out a minute after the other, they will have different temperatures: T1 and T2. The kitchen air, T3, will be different again.

After some time, having cooled down, the temperature of the cupcakes will be the same as that of the kitchen: T1 = T3 and T2 = T3.

The cupcakes have therefore reached the same temperature (T1 = T2) or a "thermal equilibrium".

The first law of thermodynamics

The first law of thermodynamics says that 'the energy of an object or system that is isolated remains constant' and that 'the energy in the system can be transformed but not destroyed '.

This can be expressed by the following formula:

$∆U=Q-W$

Here ΔU is the change in the object's energy or 'internal energy', while ' W ' and ' Q ' are the heat and the work consumed or produced by the object.

This law is an energy conservation law, as the energy of an object will change only if the object produces or receives work or radiates or obtains heat.

For example, when you heat water in the oven, the internal energy of the water will increase as the molecules start moving faster. This increase is caused by the heat of the oven. In this case, the water does not produce any work.

The second law of thermodynamics

The second law of thermodynamics specifies the direction in which energy flows. The German scientist Rudolf Clausius wrote,

We are all used to heat escaping when we open the window on a cold day or the oven door after baking. Less intuitively or logically, however, machines that produce work are unable to convert 100% of the fuel into work. The implications of the second law of thermodynamics are as follows:

• A machine or system always experiences a non-recoverable heat loss.
• The loss of heat or energy is part of an ' irreversible process ', which is to say that it cannot be reversed without using more energy.
• This irreversibility is measured by a variable called entropy, whose symbol is 'S'.

The third law of thermodynamics

The third law of thermodynamics links the temperature of a system with the atomic order of the system and its energy and says that 'the entropy of a system at zero absolute is constant'. In this case, the entropy of the system is its disorder.

What are engines?

In thermal engineering, engines are machines that use thermal energy to produce work or use work to modify the system's thermal energy.

We can see some examples below:

• An air conditioning system is a cooling machine, which uses electrical energy to pass the air of the room through a series of tubes containing a liquid or gas that absorbs the heat of the air, releasing it out of the room.
• A combustion engine in a car is a thermal engine, as it uses gas and an electrical spark to produce a controlled explosion that generates energy and heat. The energy of the explosion is transformed into movement using the car's mechanical components. This movement of the car is what we call 'work'.

See also the following diagrams of a cooling machine (left) and a heat engine (right):

Figure 2.- Examples of thermodynamic machines: The freezer (left) uses energy 'Q' to produce work 'W', which extracts heat from inside the freezer, thus lowering its temperature. The heat engine (right) uses heat from a heat reservoir to produce work, which is converted into energy. Source: Manuel R. Camacho for StudySmarter.

Thermodynamics and Engines: Efficiency of an engine

Efficiency concerns the amount of work done with the energy used. When more energy is required to do the same amount of work, the engine is less efficient. When less energy is required, the engine is more efficient. As we can measure the energy used in heat units (joules or calories), the efficiency of an engine can be expressed as follows:

$\eta =\frac{W}{Q}$

Here ' W ' is the work done by the machine in joules, while ' Q ' is the energy used by the machine, also in joules. Regarding the efficiency of an engine, note that:

• Efficiency has no units and is known as dimensionless.
• The minimum efficiency for any work done is 0.
• Efficiency cannot be larger than 100%.

We can also calculate a thermal efficiency that is equal to the difference between heat input 'Qin' and heat output 'Qout':

$\eta =\frac{Q_{in}-Q_{out}}{Q_{in}}$

The difference between the heat input and output is the work done by the engine:

$\eta =\frac{W}{Q_{in}}$

In the following calculations, the work and heat are both given in joules:

Thermodynamics and Engines: Thermodynamic cycles

A thermodynamic cycle is a series of processes performed by a thermal engine that involve heat and work. A thermodynamic cycle is a system in which four variables change: the volume ' V ', the pressure 'P ', the entropy ' S ', and the temperature ' T '. The changes are the result of changes in the internal energy, the work produced or received, or the heat produced or received. Examples of thermodynamic cycles include:

• Carnot cycle.
• Otto cycle.
• Stirling cycle.
• Ericsson cycle.
• Rankine cycle.
• Diesel cycle.
• Brayton cycle.

Each cycle is composed of four steps: compression of a fluid, heat addition to the fluid, expansion of the fluid, and heat rejection by the fluid.