Thermodynamics and engines (3.11.2)

The first law of thermodynamics, also known as the law of conservation of energy, states that energy in a system can neither be created nor destroyed.

Energy can be transferred through heating, cooling, or doing work.

The energy transferred to the system can be positive or negative:

• Positive indicates energy is transferred into the system (such as through heating).
• Negative indicates energy is transferred away from the system (through cooling).

The work done by the system can be either positive or negative:

• Positive indicates work is done by the system (when a gas expands as it is heated).
• Negative indicates work is done on the system (when gas is compressed).

Internal energy is the sum of the kinetic energy and potential energy of every particle in the system.

The change in internal energy can be positive or negative.

• Positive indicates an increase in the kinetic energy and/or the potential energy of the particles. This can occur when heating a gas.
• Negative indicates a decrease in the kinetic energy and/or the potential energy of the particles. This can occur during the cooling of a gas.

In a closed system, any changes that occur are non-flow processes, with no mass exchange with the surroundings. To use the first law of thermodynamics on non-flow processes, the gas inside must be considered an ideal gas.

Treating a system as an ideal gas means that:

• any collisions of particles are perfectly elastic (conserve energy), and
• there are no intermolecular forces acting between particles.

The absence of intermolecular forces implies that the system has no potential energy. Therefore, the internal energy is equal to the sum of only the kinetic energies of all the particles. This means that internal energy only depends on the temperature of the gas.

An example of an adiabatic process is the rapid expansion of a gas in a piston, where no heat is exchanged with the surroundings. As the gas expands rapidly, it performs positive work on its surroundings, thereby decreasing its internal energy.

Since internal energy depends only on temperature, a change in temperature must occur.

An example of an isochoric process is the heating of a gas in a rigid, sealed container, such as a pressure cooker.

As heat is added to the gas, its temperature increases, leading to a rise in pressure within the container. Since the volume does not change, no work is done on or by the gas during this process. The energy transferred as heat effectively increases the gas’s internal energy.

Pressure–volume (P–V) diagrams can represent non-flow processes. Arrows on the diagram indicate the changes that occur in the system, and the area beneath the curve shows the work done during the process.

It is useful to note that an increase in volume indicates that work is being done by the system (expansion), while a decrease in volume implies that work is being done on the system (compression).

For an adiabatic process, no energy is transferred in or out of the system and the first law of thermodynamics reduces to:

Additionally, the ideal gas equation during an adiabatic process is:

The P–V curve for such an expression has the form:

For an isothermal process, the temperature of the system is kept constant, , and the first law of thermodynamics reduces to:

Additionally, during an isothermal process, the ideal gas equation becomes:

The P–V curve for this process has the form:

The P–V curves for isothermal processes are similar to those for adiabatic processes, but they have a less steep gradient. The area under the isothermal curve is greater than that under the adiabatic curve, so the gas does more work when it expands isothermally than when it expands adiabatically.

In an isobaric process, the system’s pressure is kept constant. Hence, the P–V curve for this process has the form:

The area under isobaric P–V diagrams is the work done, where only the volume changes:

• if the volume increases, work is done by the gas,
• if the volume decreases, work is done on the gas.

In an isochoric process, the system’s volume is kept constant. Hence, the P–V curve for this process has the form:

No work is done, and the P–V curve has no area under it. For example, no work is done by or on a gas when its pressure increases from state A to state B at constant volume.

Cyclic processes occur when a system undergoes two or more processes, one after the other, and returns to the original volume, temperature and pressure. The process forms a loop.

The total work done by the system is the area inside the loop. In the example above, the gas undergoes:

• isobaric expansion from state 1 to state 2,
• isochoric cooling from state 2 to state 3,
• isobaric compression from state 3 to state 4, and
• isochoric heating from state 4 back to state 1.

It is important to note that cyclical processes can be repeated; this is the principle behind engines. For this, the energy done by the system is greater than the energy done on the system.

Internal combustion engines are used in cars. A four-stroke petrol engine burns fuel once every four strokes of the internal piston. A stroke is a single movement of the pistons, either up or down.

The engine’s cylinder (or system) undergoes a sequence of events to produce energy. This is called the Otto cycle.

The Otto cycle describes the sequence a cylinder undergoes in a combustion engine.

1. Induction: The piston starts at the top and moves down, increasing the system’s volume. This allows more gas to be drawn into the inlet valve. The pressure remains constant.
2. Compression: The inlet valve is closed, and the piston moves back up. This does work on the gas. This is done in an adiabatic process, where the volume decreases and the pressure increases.
   At the end of the stroke, the fuel–air mixture inside the cylinder is ignited by a spark plug. The temperature and pressure suddenly increase at an almost constant volume.
3. Power (Expansion): The gas ignites, and high pressure forces the piston back down the cylinder, and the expanding gas does work. The pressure reduces as the piston is forced back down.
4. Exhaust: The piston comes back up the cylinder, and the burnt gas is forced out of an exhaust valve.

The indicator diagram for a four-stroke petrol engine uses the assumptions that:

• The same gas is cycled through the engine.
• All pressure and temperature changes are instantaneous.
• All expansion and compression occurs adiabatically.
• There is no friction in the engine.
• The heat source is external.

An example of a theoretical indicator diagram looks like:

This is a cyclical process.

• gas is compressed adiabatically.
• ignition occurs and heat is supplied, the volume stays constant.
• gas expands adiabatically.
• system is cooled at a constant volume.

The cycle forms a loop. The work done by the gas equals the area inside the loop.

The real indicator diagram for the four-stroke petrol engine is shown below.

The cyclical process is described below:

• air is taken in (induction).
• the gas is compressed (spark is induced near the end of the stroke).
• the gas expands.
• air is pushed out of the system (exhaust).

The work done by the air-fuel mixture is the area enclosed in the loop.

It is important to note that the work done on the real indicator diagram is always less than the loop enclosed on a theoretical indicator diagram, as the assumptions discount energy losses in the system.

There are key differences between the theoretical and real indicator diagrams for the four-stroke petrol engine.

The main differences between theoretical and real-life diagrams are:

1. The corners of real diagrams are rounded. This is because it takes time for the valves to open and shut; the theoretical diagram assumes this is instantaneous.
2. The heating and cooling in real diagrams do not occur at constant volume.
3. Expansion and compression in real diagrams are not adiabatic, as heat transfer occurs during the piston’s strokes.
4. In a real engine, the gas is not pure air. It has exhaust fumes in it, too.
5. In the theoretical diagram, the induction and exhaust strokes are not included.

Diesel engines are different from petrol engines. They still use a four-stroke system, but the process cycle is different.

1. Induction: only air is drawn in through the intake valve; a petrol engine intakes a mixture of petrol and air.
2. Compression: The air is compressed to a high temperature, which vaporises and ignites the diesel fuel pumped directly into the cylinder through an injector.
3. Power (Expansion): The gas ignites, and high pressure forces the piston back down the cylinder, and the expanding gas does work. The pressure reduces as the piston is forced back down.
4. Exhaust: The piston comes back up the cylinder, and the burnt gas is forced out of an exhaust valve.

It is important to note that the power and exhaust stages are the same as a petrol engine.

A diesel engine has a theoretical indicator diagram that looks like:

• gas in compressed in an adiabatic process.
• the gas is heated at a constant pressure.
• the gas expands adiabatically.
• the system cools at a constant volume.

In reality, the actual indicator diagram of a diesel engine looks like:

The induction and exhaust processes occur at a constant pressure. The work done is the area enclosed by the loop.

Diesel engines are generally more efficient than petrol engines. Efficiency in internal combustion engines is closely related to the compression ratio during the compression stroke.

The compression ratio on an indicator diagram is the ratio:

• Diesel engines have a larger, more efficient compression ratio, allowing the higher pressures and temperatures needed for self-ignition.
• Petrol engines use a spark plug and must avoid high pressure and temperature to prevent pre-ignition (self-ignition), which can be caused by carbon buildup.

Producing diesel engines is more expensive because they must withstand higher pressures. However, petrol engines pose greater environmental issues, producing more hydrocarbons, and than diesel engines, even with a catalytic converter.

In a four-stroke engine, one complete cycle of operation consists of four distinct strokes: induction, compression, power, and exhaust. The entire cycle requires two revolutions of the crankshaft. This is because:

• the induction and compression strokes take one revolution, and
• the power and exhaust strokes take one revolution.

The indicated power is equal to the work done by the engine per second. The work done equals the area of the main P–V loop on the indicator diagram. Hence, the overall indicated power of an engine is:

The second law of thermodynamics states that no real engine can convert all the heat it takes in into useful work; some energy will always be lost as waste heat.

Additionally, the second law requires that a heat engine operate between a heat source (such as a hot engine) and a heat sink (such as the air or water). For the engine to work well, it needs to draw heat from the hot source and release some heat to the cooler sink, leading to inefficiencies.

It is important to note that a heat engine cannot work solely on the principle of the first law of thermodynamics. If no work is done, then no power can be generated. Frictional forces mean that an engine can not be 100% efficient.

All engines must have a source and a sink to obey the second law of thermodynamics. For the engine to work well, it needs to draw heat from the hot source and release some heat to the cooler sink.

The main features of a source–sink engine:

1. Heat energy is transferred from the hot source at temperature to the heat engine.
2. Some of the energy is transferred into work – but there are losses.
3. The remaining energy is transferred to the sink at a lower temperature .
   The relation between the three quantities can be written as:

We calculate the efficiency of an engine using the ratio of the supplied heat energy and the useful work output:

The maximum theoretical efficiency is calculated by assuming the system uses an ideal gas. We can rewrite the above equation as:

Where

• is the temperature of the source, and
• is the temperature of the sink.

The theoretical efficiency will always exceed the actual efficiency as real heat engines have imitations:

• Work is done internally to overcome friction.
• Incomplete fuel combustion limits the temperature rise in the engine.
• Useful power is wasted to drive internal motors and pumps.
• The fuel mixture is not an ideal gas.

The processes in a heat engine are irreversible, so energy is always dissipated in the system.

Heat engines are inefficient. The amount of energy transferred to the sink is usually higher than the useful work output .

To counteract this, methods have been developed to maximise and minimise the energy transferred to the sink or to utilise this wasted energy. An example of this are combined heat and power (CHP) schemes.

CHP schemes take advantage of the large amount of heat transferred from power stations to cooling towers by redirecting it for use in homes and local businesses.

Reverse heat engines transfer heat energy from a cold sink to a hotter source.

The second law of thermodynamics states that heat naturally flows from hot to cold, so to go the opposite direction, work must be done.

Examples of reverse heat engines include:

• Refrigerators or air conditioning units: They extract energy from the cold region (the sink) by pumping heat into the room (the source).

• Heat pumps: They transfer energy to the hot region (a house) by cooling the outdoors.