7.4 Engine Cycles, Latent Heat & Heat of Combustion

Engine Cycles, Latent Heat & Heat of Combustion

Thermodynamics becomes “engines and ice” when you connect gas processes into cycles, reverse heat flow with refrigerators and heat pumps, account for latent heat during changes of state, and quantify fuel energy through heat of combustion. Module 2 stays conceptual: you are not designing a full Otto-cycle analysis for certification, but you must recognise process types, state-change energy, and what combustion energy means for propulsion and APU/ground power thinking.

Isothermal vs Adiabatic Processes

Isothermal

An isothermal process occurs at constant temperature. For an ideal gas, internal energy U depends only on temperature, so ΔU = 0 in a purely isothermal process. From the first law, Q = W: heat absorbed equals work done by the gas during isothermal expansion (and the reverse for compression). Boyle’s law applies: PV = constant along an ideal-gas isotherm.

True isothermal behaviour needs enough time and heat transfer with a thermal reservoir to hold T fixed. Slow compression with cooling can approximate it; rapid processes usually do not.

Adiabatic

An adiabatic process has no heat transfer: Q = 0. Insulation, or a process so fast that little heat crosses the boundary, approximates adiabatic behaviour.

From the first law with Q = 0: ΔU = −W.

• Adiabatic expansion: gas does work, internal energy falls, temperature falls.
• Adiabatic compression: work is done on the gas, internal energy rises, temperature rises.

That is why a bicycle pump warms when you compress air quickly, and why expanding gas from a high-pressure bottle feels cold at the outlet. In engines, compression heats the charge before combustion; expansion extracts work and the gas cools.

For ideal gases, adiabatic reversible relations involve γ = Cp/Cv (e.g. TV^{γ−1} = constant forms) — recognise that T and P change with V even without heat, unlike the isothermal case.

Idealised Engine Cycles (Module 2 Depth)

A heat engine absorbs heat from a hot source, does net work, and rejects waste heat to a cold sink — second-law compatible. Piston engines are often idealised with simple process loops on a P–V diagram.

Constant-volume heat addition (Otto-like concept)

The classic Otto cycle idealisation (spark-ignition style thinking) includes:

1. Adiabatic compression of the mixture
2. Heat addition at constant volume (approximating rapid combustion while the piston is near top dead centre — volume almost fixed)
3. Adiabatic expansion (power stroke)
4. Heat rejection at constant volume

Constant-volume heating means the piston is not moving during the idealised heat-add step: pressure and temperature jump up as chemical energy becomes thermal energy in the gas. No expansion work occurs during that instant of heat add; work is extracted mainly during the expansion stroke.

Module 2 takeaway: spark-ignition idealisation ↔ heat addition at nearly constant volume.

Constant-pressure heat addition (Diesel-like concept)

The classic Diesel cycle idealisation (compression-ignition style thinking) includes:

1. Adiabatic compression of air (high ratio → high T)
2. Heat addition at constant pressure (fuel injected and burned while the piston moves, idealised so pressure stays roughly constant)
3. Adiabatic expansion
4. Heat rejection at constant volume (simplified end of exhaust/idealisation)

Constant-pressure heating allows expansion work during heat addition (W = PΔV along that leg) as well as during the main expansion. Module 2 takeaway: diesel idealisation ↔ heat addition at constant pressure after high compression.

Real engines are messier (finite burn time, heat losses, valve overlap). Exam level: name the idealised heat-addition constraint and link it to Otto vs Diesel teaching models.

Why cycles matter to maintenance physics

• Compression raises T before ignition or injection — adiabatic-like compression heating.
• Combustion adds chemical energy → high P and T → expansion does work on the piston or turbine.
• Exhaust rejects heat; cooling systems remove heat that did not become work (first and second laws in practice).
• Efficiency improves conceptually with higher peak temperatures and compression within material limits — never unlimited because of the second law and materials.

Refrigerators and Heat Pumps

A refrigerator removes heat from a cold space and dumps heat to a warmer environment. A heat pump uses the same physics, often emphasising useful heat delivered to a warm space. Both require work input (compressor, etc.).

Energy balance sketch (magnitudes):

Q_hot = Q_cold + W_in

Heat rejected to the hot side exceeds heat taken from the cold side by the work supplied. This does not break the second law: heat is not flowing spontaneously cold → hot; the compressor organises the cycle (vapour-compression: evaporation absorbs latent heat at low pressure/temperature; condensation rejects heat at higher pressure/temperature).

Aircraft examples:

• Vapour-cycle air conditioning packs (where fitted) — refrigeration cycle cools cabin air.
• Air-cycle machines on many transport aircraft — different machinery but same goal: move heat and control cabin temperature using work extracted from bleed or electric power.
• Galley refrigeration and some equipment cooling.

Performance is often discussed as coefficient of performance (COP) rather than “efficiency” like a heat engine; Module 2 mainly needs the direction of heat, the necessity of work, and the link to latent heat in evaporators/condensers.

Latent Heat: Fusion and Vaporisation

Latent heat is the heat energy absorbed or released during a change of state at constant temperature (for a pure substance at fixed pressure).

Latent heat of fusion (L_f)

Energy to change solid ↔ liquid at the melting/freezing point:

Q = m L_f

• Melting (fusion): system absorbs Q
• Freezing: system releases Q

Ice at 0 °C absorbing heat does not rise above 0 °C until all ice is melted (ideal pure case). That energy is latent, not sensible.

Latent heat of vaporisation (L_v)

Energy to change liquid ↔ vapour at the boiling/condensation point:

Q = m L_v

• Boiling/evaporation: absorbs large Q (water’s L_v is very large — about 2.3 MJ/kg order at 100 °C)
• Condensation: releases the same magnitude of heat

Worked example — vaporisation. Mass 0.50 kg of water fully vaporised at constant temperature; L_v = 2.3 × 10⁶ J/kg.

Q = m L_v = 0.50 × 2.3 × 10⁶ = 1.15 × 10⁶ J = 1.15 MJ

Latent heat in systems

• Sweat and evaporative cooling: liquid water absorbs L_v from skin/air.
• Refrigerant evaporator: liquid refrigerant absorbs latent heat from cabin air path.
• Condenser: refrigerant vapour releases latent heat to outside air or ram air.
• Carburettor icing awareness (Module 2 + systems): fuel vaporisation and pressure drop cool the throttle region — latent heat and expansion cooling can freeze moisture.

Sensible heat changes temperature; latent heat changes state. Both are energy in joules.

Thermal Energy and Heat of Combustion

Thermal energy in Module 2 language often means the internal energy associated with the random motion and microscopic potential energy of particles — the energy content that temperature and state reflect. Heating, cooling, and combustion rearrange and transfer this energy.

Heat of combustion (enthalpy of combustion / calorific value in engineering speech) is the heat energy released per unit mass (or per mole) of fuel when the fuel burns completely under stated conditions (and with stated H₂O product phase for “higher” vs “lower” heating value — awareness only).

Q_released ≈ m_fuel × (heat of combustion)

Example scale: hydrocarbon aviation fuels release on the order of 4 × 10⁷ J/kg (tens of MJ/kg). Exact table values vary by fuel; exam questions give the figure when needed.

Worked example — combustion energy. Burn 0.020 kg of fuel with heat of combustion 43 MJ/kg.

Q = 0.020 × 43 = 0.86 MJ = 860 kJ released as thermal energy in the combustion products (ideal complete combustion bookkeeping). Only a fraction becomes useful shaft or propulsive work; the rest is exhaust and cooling heat — first and second laws again.

Linking combustion to cycles

1. Fuel’s chemical energy → heat of combustion during burn.
2. Working gas internal energy and pressure rise (constant V or P idealisation).
3. Expansion → work on piston/turbine.
4. Rejected heat to exhaust and coolers.

Maintenance implications: correct mixture, atomisation, and combustion completeness affect whether the fuel’s calorific value is realised; cooling systems must reject the large waste-heat share; fire protection respects the energy density of fuel.

Integrated Picture

• Isothermal: T fixed; ideal gas PV = constant.
• Adiabatic: Q = 0; expansion cools, compression heats.
• Otto-like: heat add at constant volume; Diesel-like: heat add at constant pressure (ideal teaching models).
• Fridge/heat pump: work moves heat cold → hot.
• Latent heat: Q = mL for fusion/vaporisation at constant T.
• Heat of combustion: chemical energy per mass available as heat when fuel burns.

Formula Recap

• Adiabatic: Q = 0; ΔU = −W
• Isothermal ideal gas: ΔU = 0; Q = W (expansion)
• Const pressure work: W = PΔV
• Latent: Q = m L_f or m L_v
• Combustion energy scale: Q = m × (heat of combustion)
• Refrigerator balance: Q_hot = Q_cold + W_in

With temperature, heat transfer, gas laws, cycles, and latent/combustion energy in place, Module 2 thermodynamics covers Appendix I 2.3 from thermometer scales to engine-cycle concepts used across airframe and powerplant systems.