How is Heat Transferred?
25 April, 2022
To understand the workings of compressed air, a basic introduction to physics can come a long way. Learn more about thermodynamics and how they are vital in understanding how air compressors work.
Air compressor thermodynamics explained
Air compressor thermodynamics explains how electrical energy becomes pressure energy, why compression creates heat, and how that heat can be reused. In this article we will cover the Boyle's and Charles' gas laws, operating effects, discharge temperatures, and energy recovery potential.
Thermodynamics laws for compressor energy and entropy
Applying thermodynamic principles to air compressors requires treating the system as an open system (control volume) with constant mass flow, shaft power, and heat transfer. The overall system behavior depends on the balance of these energetic inputs and outputs.
First law of thermodynamics applied to air compressors
The first law states that energy is conserved. In steady operation, the electrical power delivered to the compressor motor (kW) appears as an increase in the air’s enthalpy plus heat rejected through oil and air coolers. In simplified terms, shaft power raises pressure and temperature, while a significant fraction is removed as heat to keep discharge temperatures within design limits.
For example:
A typical motor input of 400 kW corresponds to exactly 400 kJ/s of energy entering the compressor package before system losses. This energy must either remain in the compressed air stream as heat or be extracted by water or air cooling circuits.
Understanding this energy balance is essential for analyzing thermodynamics and heat transfer across the system.
Second law, entropy and efficiency losses
The second law of thermodynamics explains why real compression is irreversible through entropy generation. In compressors and piping networks, friction, pressure drops, throttling, non-ideal compression paths, and heat transfer across finite temperature differences all increase entropy. These irreversibilities raise the required shaft power or electrical kW needed to deliver a target pressure and flow, while inevitably converting part of the input energy into low-grade waste heat rejected to ambient air or cooling water.
Thermodynamic concepts and compressor implications
The following concept mapping table illustrates the relationship between thermodynamic principles and the physical realities of a compressed air installation.
| Thermodynamic concept | Physical definition | Practical compressor implication |
First Law |
Total energy is conserved within a closed or steady-state open system. |
Shaft work input converts into gas enthalpy and rejected thermal energy. |
Second Law |
Heat naturally transfers from higher to lower temperature regions. |
Air must undergo cooling using external sinks (air or water loops). |
Entropy |
A measure of molecular disorder and irreversible energy degradation. |
Irreversibilities raise specific power consumption ($kW$) for the same flow. |
Reversibility |
An idealized process without losses, representing peak thermodynamic efficiency. |
Serves as the benchmark for comparing real compression stages. |
Boyle's and Charles' gas laws
Boyle’s and Charles’s laws describe the relationships between pressure, volume, and temperature in gases under idealized conditions. These gas behavior equations help engineers estimate changes during compression, predict thermal loads, and size downstream equipment.
Boyle’s law
Boyle's law states that if the temperature is constant (isotherm), then the product of the pressure and volume are constant.
p·V = constant
p₁·V₁ = p₂·V₂
Pressure (p, bar) varies inversely with volume (V, m³) when temperature is constant.
Charles’s law
Charles's law says that at constant pressure (isobar), the volume of a gas changes in direct proportion to the change in temperature.
V/T = constant
V₁/T₁ = V₂/T₂
Volume is proportional to absolute temperature (T, measured in K) at constant pressure.
Conversion: T [K] = T [°C] + 273.15.
Combined gas law
The general law of state for gasses is a combination of Boyle's and Charles's laws. This states how pressure, volume and temperature will affect each other. When one of these variables is changed, this affects at least one of the other two variables.
(p·V)/T = constant
(p₁·V₁)/T₁ = (p₂·V₂)/T₂
Ideal gas equation
The individual gas constant R only depends on the properties of the gas. If a mass m of the gas takes up the volume V, the relation can be written:
p·V = m·R·T
where m is mass and R is the specific gas constant (gas‑dependent).
Temperature and pressure changes during real compression
Real compressor packages deviate from ideal isothermal pathways because the compression process occurs too quickly for heat to escape, resulting in a polytropic process. This rapid pressure increase causes a significant temperature rise at the discharge stage, requiring aftercoolers to extract the heat before the air enters the piping network. Without cooling, the increased thermal load can damage pneumatic components and degrade downstream process lines.
Compressor thermodynamics & energy recovery
Heat of compression recovery provides a significant opportunity to offset primary heating fuels in industrial manufacturing. Capturing this thermal energy before it is rejected to the atmosphere directly reduces the utility costs of the facility.
How to estimate annual savings from heat recovery
A transparent calculation structure helps engineers validate claims:
- Recoverable heat power (kWₜₕ) = Motor power (kW) × Recovery fraction
- Annual recovered energy (kWhₜₕ/year) = kWₜₕ × Operating hours (h/year)
- Annual cost savings (€/year) = kWhₜₕ × Displaced energy price (€/kWh) × Utilisation factor
For example:
A 400 kW compressor with 90 % recoverable heat, operating 6,000 h/year, yields approximately 2.16 GWhₜₕ/year of usable heat. The monetary savings depend primarily on annual hours and the price of the displaced energy source; all assumptions are site‑specific and must be verified.
Heat sink options and temperature constraints
Process hot water temperatures between 70°C and 90°C can be reliably achieved by transferring heat from the cooling loop. This recovered thermal energy is commonly utilized for steam boiler pre-feeding, direct process heating in food production, or facilities space heating. The practical maximum temperature is governed by the compressor discharge limit and the design of the internal cooling heat exchangers.
An energy recovery control unit must be installed between the compressor cooling circuit and the external water loop. This specialized hardware dynamically regulates water flow rates and approach temperatures to maintain stable compressor operation. Proper system design prevents overcooling, which could cause premature component wear. Implementing integrated energy recovery systems ensures that hot water generation occurs reliably without degrading compressed air production.
Explore efficient compressor options
Compare compressor options using delivered flow in m³/h or l/s, working pressure in bar, load profile and specific energy in kWh/m³. If heat recovery is a project objective, evaluate recovery capability at package level, including available recovery fraction, hot-water temperature, controls and integration requirements.
Frequently asked questions
How do Boyle's law and Charles's law explain temperature rise during air compression?
During compression, reducing the air's volume increases its pressure and temperature because energy is transferred into the gas as mechanical work. According to the combined gas law, forcing a gas into a smaller volume raises its pressure, which simultaneously drives up its kinetic energy and absolute temperature unless continuous cooling occurs.
What is heat of compression in an air compressor, and where does that energy go?
The heat of compression is the thermal energy generated as a direct byproduct of compressing gas molecules into a smaller volume. In a standard system, nearly all of this energy is rejected as waste heat through aftercoolers, oil coolers, or directly to the surrounding air, but it can be recovered and utilized.
How much compressor waste heat can realistically be recovered, and what assumptions matter?
Up to 94% of input electrical energy can be successfully recovered in water-cooled systems. This recovery rate assumes the compressor runs continuously under loaded conditions, the thermal system matches a continuous process demand, and piping is designed to minimize convective heat losses to the atmosphere.
What hot-water temperatures can energy recovery deliver from a compressor, and what limits them?
Recovered water loops can reach temperatures between 70°C and 90°C. The practical limit is dictated by the compressor's maximum discharge temperature, the heat exchanger's approach temperature, and the flow rate required to maintain a stable thermal transfer without causing system overheating.
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