HVAC Systems Encyclopedia

A comprehensive encyclopedia of heating, ventilation, and air conditioning systems

Laws Principles

Thermodynamic laws govern all HVAC system operations. These fundamental principles dictate energy transfer limits, efficiency boundaries, and system performance characteristics.

Zeroth Law of Thermodynamics

Statement: If two bodies are each in thermal equilibrium with a third body, they are in thermal equilibrium with each other.

Application: Foundation for temperature measurement. Enables use of thermometers and temperature sensors in HVAC control systems. Justifies placement of temperature sensors in airstreams and refrigerant lines.

First Law of Thermodynamics

Energy Conservation Principle: Energy cannot be created or destroyed, only converted from one form to another.

General Form

For a closed system:

ΔU = Q - W

Where:

  • ΔU = change in internal energy (Btu or kJ)
  • Q = heat added to system (Btu or kJ)
  • W = work done by system (Btu or kJ)

Open System Form

For steady-flow processes (typical in HVAC):

Q̇ - Ẇ = ṁ[(h₂ - h₁) + (V₂² - V₁²)/2 + g(z₂ - z₁)]

Where:

  • Q̇ = heat transfer rate (Btu/hr or kW)
  • Ẇ = power (Btu/hr or kW)
  • ṁ = mass flow rate (lb/hr or kg/s)
  • h = specific enthalpy (Btu/lb or kJ/kg)
  • V = velocity (ft/s or m/s)
  • z = elevation (ft or m)

For HVAC applications, kinetic and potential energy changes are negligible:

Q̇ - Ẇ = ṁ(h₂ - h₁)

HVAC Applications of First Law

Cooling Coils:

Q̇ = ṁₐᵢᵣ(hₐᵢᵣ,ᵢₙ - hₐᵢᵣ,ₒᵤₜ) = ṁᵣₑf(hᵣₑf,ₒᵤₜ - hᵣₑf,ᵢₙ)

Heating Coils:

Q̇ = ṁₐᵢᵣ(hₐᵢᵣ,ₒᵤₜ - hₐᵢᵣ,ᵢₙ) = ṁwₐₜₑᵣ cₚ(Twₐₜₑᵣ,ᵢₙ - Twₐₜₑᵣ,ₒᵤₜ)

Compressors:

Ẇcₒₘₚ = ṁᵣₑf(h₂ - h₁)

Where h₂ = discharge enthalpy, h₁ = suction enthalpy

Air Handling Units (Energy Balance):

Q̇cₒₒₗᵢₙ𝓰 + Q̇ᵣₑₕₑₐₜ + Ẇfₐₙ = ṁₐᵢᵣ(hₒᵤₜ - hᵢₙ)

Second Law of Thermodynamics

Fundamental Principle: Heat flows spontaneously from hot to cold. All real processes are irreversible and generate entropy.

Kelvin-Planck Statement

Statement: It is impossible to construct a device operating in a cycle that produces no effect other than extracting heat from a reservoir and producing an equivalent amount of work.

HVAC Implication: No heat engine (including vapor-compression cycles) can achieve 100% thermal efficiency. Heat rejection is mandatory.

Consequence for Refrigeration:

COP = Qₑᵥₐₚ/Wᵢₙ < ∞

Practical vapor-compression systems: COP = 2 to 5

Clausius Statement

Statement: It is impossible to construct a device operating in a cycle that transfers heat from a cold body to a hot body without external work input.

HVAC Implication: Refrigeration and air conditioning require compressor work. Cooling cannot occur spontaneously from cold to hot.

Mathematical Expression:

∮(δQ/T) ≤ 0

Equality holds for reversible processes; inequality for irreversible processes.

Entropy

Definition: Entropy (S) is a thermodynamic property representing energy dispersion or disorder.

Entropy Change

For reversible process:

dS = δQᵣₑᵥ/T

For irreversible process:

dS > δQ/T

Entropy Generation:

Sₑₙ = ΔSₛᵧₛₜₑₘ - Q/Tᵦₒᵤₙᵈₐᵣᵧ ≥ 0

Where Sₑₙ = entropy generation (always positive for real processes)

HVAC Applications of Entropy

Refrigeration Cycle Analysis:

Ideal (reversible) cycle: ΔScᵧcₗₑ = 0

Real cycle: ΔScᵧcₗₑ > 0 due to:

  • Compressor inefficiencies
  • Pressure drops in lines
  • Heat transfer across finite temperature differences
  • Throttling in expansion valve

Mixing Processes:

When two airstreams mix:

Sₑₙ = ṁ₁s₃ + ṁ₂s₃ - ṁ₁s₁ - ṁ₂s₂ > 0

Mixing is always irreversible and generates entropy.

Heat Exchanger Analysis:

Entropy generation in heat exchanger:

Sₑₙ = ṁcₒₗᵈ(sₒᵤₜ - sᵢₙ)cₒₗᵈ + ṁₕₒₜ(sₒᵤₜ - sᵢₙ)ₕₒₜ > 0

Lower entropy generation indicates better heat exchanger design.

Reversibility and Irreversibility

Reversible Process

Characteristics:

  • No friction
  • Infinitely slow (quasi-equilibrium)
  • No finite temperature differences
  • No dissipative effects

Reality: No real process is reversible. Reversible processes represent theoretical limits.

Irreversibilities in HVAC Systems

Major Sources:

  1. Friction: Fluid flow through ducts, pipes, valves, fittings
  2. Heat Transfer: Across finite temperature differences in coils, heat exchangers
  3. Throttling: Expansion valves in refrigeration cycles (isenthalpic process with entropy increase)
  4. Mixing: Different temperature airstreams
  5. Compression/Expansion: Non-ideal compressor and turbine processes
  6. Combustion: Burner inefficiencies

Quantification:

Exergy destruction due to irreversibility:

Ẋdₑₛₜᵣₒᵧₑᵈ = T₀Sₑₙ

Where T₀ = ambient temperature (°R or K)

Carnot Cycle Efficiency Limits

Carnot Heat Engine

Maximum theoretical efficiency:

ηCₐᵣₙₒₜ = 1 - Tcₒₗᵈ/Tₕₒₜ

Temperatures must be in absolute scale (°R or K)

Carnot Refrigerator

Maximum theoretical COP:

COPCₐᵣₙₒₜ,ᵣₑf = Tcₒₗᵈ/(Tₕₒₜ - Tcₒₗᵈ)

Example:

Refrigeration system: Tₑᵥₐₚ = 40°F (500°R), Tcₒₙᵈ = 100°F (560°R)

COPCₐᵣₙₒₜ = 500/(560 - 500) = 8.33

Actual system COP = 3.0 to 4.0 (much lower due to irreversibilities)

Carnot Heat Pump

Maximum theoretical COP:

COPCₐᵣₙₒₜ,ₕₚ = Tₕₒₜ/(Tₕₒₜ - Tcₒₗᵈ)

Note: COPₕₚ = COPᵣₑf + 1

Clausius Inequality

For any cycle:

∮(δQ/T) ≤ 0
  • Equality: reversible cycle
  • Inequality: irreversible cycle

Application: Establishes entropy as a property. Enables calculation of entropy changes for any process by integrating along reversible path between same states.

Third Law of Thermodynamics

Statement: The entropy of a pure crystalline substance at absolute zero temperature is zero.

HVAC Relevance: Provides reference point for absolute entropy values used in thermodynamic property tables (negligible practical impact on HVAC calculations).

Practical Implications for HVAC Design

System Efficiency Limits

First and second laws establish:

  1. Energy must balance (First Law): All inputs must equal outputs
  2. Quality degrades (Second Law): Cannot achieve 100% efficiency in energy conversion

Performance Optimization

Reduce Irreversibilities:

  • Minimize pressure drops (larger ducts/pipes, fewer fittings)
  • Reduce temperature differences in heat exchangers (larger surface area)
  • Improve compressor efficiency (reduce clearance volume, better valve design)
  • Eliminate mixing when possible (variable air volume systems)
  • Use economizers to reduce compressor work

Energy Recovery

Second law efficiency (exergetic efficiency):

ηₑₓₑᵣ𝓰ₑₜᵢc = (Exergy recovered)/(Exergy supplied)

More meaningful than first law efficiency for evaluating energy recovery systems.

Maxwell Relations

Derived from equality of mixed partial derivatives of thermodynamic potentials:

(∂T/∂v)ₛ = -(∂P/∂s)ᵥ

(∂T/∂P)ₛ = (∂v/∂s)ₚ

(∂P/∂T)ᵥ = (∂s/∂v)ₜ

(∂v/∂T)ₚ = -(∂s/∂P)ₜ

HVAC Application: Used to derive relationships between measurable properties (P, v, T) and difficult-to-measure properties (s, u, h).

Gibbs and Helmholtz Free Energy

Gibbs Free Energy:

G = H - TS

Helmholtz Free Energy:

A = U - TS

HVAC Relevance: Used in chemical thermodynamics for refrigerant property calculations and phase equilibrium determination. Essential for equation of state development.

Key Takeaways

  1. First Law: Energy balance governs all HVAC equipment sizing
  2. Second Law: Establishes efficiency limits; cooling requires work input
  3. Entropy: Quantifies irreversibility; lower entropy generation indicates better design
  4. Carnot Cycle: Theoretical maximum efficiency/COP for given temperature limits
  5. Irreversibilities: Real systems always fall short of ideal performance
  6. Optimization Strategy: Reduce entropy generation by minimizing temperature differences, pressure drops, and mixing