Processes

Thermodynamic processes describe the path a system follows as it changes from one equilibrium state to another. Understanding these processes is essential for analyzing HVAC equipment cycles, compression, expansion, heating, and cooling operations.

Fundamental Process Types

Isothermal Process (Constant Temperature)

Definition: Temperature remains constant throughout the process (T = constant, dT = 0).

Governing Relations:

For ideal gas: PV = constant
Temperature: T₁ = T₂
Internal energy change: ΔU = 0 (for ideal gas)
Heat equals work: Q = W

Work Calculation:

W = ∫PdV = mRT ln(V₂/V₁) = mRT ln(P₁/P₂)
W = P₁V₁ ln(V₂/V₁)

Heat Transfer:

Q = W = mRT ln(V₂/V₁)

HVAC Applications:

Ideal vapor compression at constant condenser/evaporator temperatures
Long-term heat exchanger processes with large thermal mass
Ground-source heat pump ground loop approximation (seasonal average)
Storage tank thermal processes with sufficient time constant

Practical Considerations:

Requires perfect heat transfer or extremely slow process
Real HVAC processes approximate isothermal behavior in large thermal mass systems
Useful idealization for phase change processes (evaporation, condensation)

Isobaric Process (Constant Pressure)

Definition: Pressure remains constant throughout the process (P = constant, dP = 0).

Governing Relations:

For ideal gas: V/T = constant
Volume ratio: V₂/V₁ = T₂/T₁
Enthalpy change: ΔH = Q (at constant pressure)

Work Calculation:

W = P(V₂ - V₁) = PΔV = mR(T₂ - T₁)

Heat Transfer:

Q = mCₚ(T₂ - T₁) = ΔH

First Law Application:

ΔU = Q - W = mCᵥ(T₂ - T₁)
Q = ΔU + W = mCₚ(T₂ - T₁)

HVAC Applications:

Heating coils (air heated at atmospheric pressure)
Cooling coils (air cooled at constant pressure)
Boiler water heating (liquid phase at constant system pressure)
Open spray chambers and humidifiers
Atmospheric air handling processes
Combustion in open furnaces

Practical Considerations:

Most air-side HVAC processes are approximately isobaric
Pressure drop in ducts/coils creates slight deviation from ideal
Enthalpy calculations directly applicable (psychrometric charts)

Isochoric Process (Constant Volume)

Definition: Volume remains constant throughout the process (V = constant, dV = 0).

Governing Relations:

For ideal gas: P/T = constant
Pressure ratio: P₂/P₁ = T₂/T₁
No boundary work: W = 0

Work Calculation:

W = ∫PdV = 0 (since dV = 0)

Heat Transfer:

Q = ΔU = mCᵥ(T₂ - T₁)

First Law Application:

Q = ΔU (since W = 0)
ΔU = mCᵥ(T₂ - T₁)

HVAC Applications:

Refrigerant in rigid closed vessel during heating/cooling
Receiver tank pressure/temperature relationships
Closed vessel safety relief valve sizing calculations
Autoclave and sterilizer initial heating phases
Refrigerant cylinder storage temperature-pressure relationships

Practical Considerations:

Common in analysis of closed storage vessels
Pressure rises directly with temperature increase
Critical for safety relief valve design
Used in refrigerant property table relationships

Isentropic Process (Constant Entropy)

Definition: Entropy remains constant throughout the process (s = constant, ds = 0). Represents an ideal reversible adiabatic process.

Governing Relations:

For ideal gas: PVᵏ = constant, TVᵏ⁻¹ = constant, TPᵏ/(¹⁻ᵏ) = constant
Specific heat ratio: k = Cₚ/Cᵥ
No heat transfer: Q = 0
Reversible: No entropy generation

Pressure-Volume Relations:

P₂/P₁ = (V₁/V₂)ᵏ

Temperature Relations:

T₂/T₁ = (V₁/V₂)ᵏ⁻¹ = (P₂/P₁)⁽ᵏ⁻¹⁾/ᵏ

Work Calculation:

W = ΔU = mCᵥ(T₂ - T₁) = [P₂V₂ - P₁V₁]/(1 - k)

For ideal gas:
W = [mR(T₁ - T₂)]/(k - 1) = [P₁V₁/(k-1)][1 - (P₂/P₁)⁽ᵏ⁻¹⁾/ᵏ]

Isentropic Efficiency:

Compression: ηc = Ws/Wa = (h₂s - h₁)/(h₂a - h₁)
Expansion: ηt = Wa/Ws = (h₁ - h₂a)/(h₁ - h₂s)

Where subscript ’s’ indicates isentropic and ‘a’ indicates actual process.

HVAC Applications:

Ideal compressor compression process (baseline for efficiency)
Ideal turbine/expander expansion process
Nozzle flow (short residence time, minimal heat transfer)
Benchmark for actual compression/expansion processes
Centrifugal and screw compressor efficiency calculations
Chiller compressor performance analysis

Practical Considerations:

Real compressors: 70-85% isentropic efficiency (reciprocating, scroll)
Real compressors: 75-85% isentropic efficiency (screw, centrifugal)
Deviations due to friction, heat transfer, irreversibilities
Used to calculate actual work from ideal work and efficiency

Polytropic Process (General Process)

Definition: A general process following the relation PVⁿ = constant, where n is the polytropic exponent.

Governing Relation:

PVⁿ = constant
P₁V₁ⁿ = P₂V₂ⁿ

Polytropic Exponent Values:

n = 0: Isobaric (constant pressure)
n = 1: Isothermal (constant temperature)
n = k: Isentropic (reversible adiabatic)
n = ∞: Isochoric (constant volume)
1 < n < k: Real compression/expansion with heat transfer

Temperature Relations:

T₂/T₁ = (V₁/V₂)ⁿ⁻¹ = (P₂/P₁)⁽ⁿ⁻¹⁾/ⁿ

Work Calculation:

W = [P₂V₂ - P₁V₁]/(1 - n) = [mR(T₂ - T₁)]/(1 - n)

For n ≠ 1:
W = [P₁V₁/(n-1)][1 - (P₂/P₁)⁽ⁿ⁻¹⁾/ⁿ]

Heat Transfer:

Q = W + ΔU = W + mCᵥ(T₂ - T₁)
Q = mCₙ(T₂ - T₁)

Where Cₙ = Cᵥ[(k - n)/(1 - n)]

HVAC Applications:

Real compressor processes (n = 1.2 to 1.3 for reciprocating with cooling)
Actual expansion processes in turbines
Compressor performance mapping
Real gas compression with jacket cooling/heating
Multi-stage compression analysis

Determining Polytropic Exponent:

n = ln(P₂/P₁)/ln(V₁/V₂) = log(P₂/P₁)/log(V₁/V₂)

Practical Considerations:

More accurate model for real compression than isentropic
Accounts for heat transfer during compression/expansion
Polytropic efficiency often used instead of isentropic for long processes
Typical reciprocating compressor: n = 1.25-1.30
Typical centrifugal compressor: n = 1.30-1.35

Adiabatic Process (No Heat Transfer)

Definition: No heat transfer occurs between system and surroundings (Q = 0, δQ = 0).

First Law Application:

Q = ΔU + W
0 = ΔU + W
W = -ΔU = -mCᵥ(T₂ - T₁)

Types:

Reversible adiabatic = Isentropic (s = constant)
Irreversible adiabatic (s increases due to friction/irreversibilities)

HVAC Applications:

Rapid compression/expansion processes
Insulated compressor analysis
Throttling valves (also isenthalpic)
Short-duration transient processes
Nozzles and diffusers (high velocity, short time)

Throttling Process (Isenthalpic)

Definition: Enthalpy remains constant (h = constant). Irreversible adiabatic process through a restriction with no work output.

Governing Relations:

Enthalpy: h₁ = h₂
No heat transfer: Q = 0
No work: W = 0
Entropy increases: s₂ > s₁ (irreversible)

Pressure and Temperature:

Pressure drops: P₂ < P₁
Temperature change depends on fluid properties
For ideal gas: T₁ = T₂ (Joule-Thomson coefficient = 0)
For real fluids: Temperature changes (Joule-Thomson effect)

Joule-Thomson Coefficient:

μJ = (∂T/∂P)h = (1/Cₚ)[T(∂V/∂T)P - V]

HVAC Applications:

Thermostatic expansion valves (TXV)
Electronic expansion valves (EEV)
Capillary tubes
Pressure reducing valves
Orifice plates and flow restrictors
Critical component in refrigeration cycles

Practical Considerations:

Causes pressure drop and typically temperature drop in refrigerants
No work recovery (irreversible process)
Enthalpy remains constant but temperature and quality change
Creates mixture of liquid and vapor in refrigeration systems

Work and Heat Calculations Summary

Boundary Work (Closed System)

W = ∫P dV

Isobaric: W = P(V₂ - V₁)
Isothermal: W = mRT ln(V₂/V₁)
Isochoric: W = 0
Isentropic: W = [P₁V₁/(k-1)][1 - (P₂/P₁)⁽ᵏ⁻¹⁾/ᵏ]
Polytropic: W = [P₁V₁/(n-1)][1 - (P₂/P₁)⁽ⁿ⁻¹⁾/ⁿ]

Heat Transfer

General: Q = ΔU + W (First Law)

Isobaric: Q = mCₚ(T₂ - T₁)
Isothermal: Q = W = mRT ln(V₂/V₁)
Isochoric: Q = mCᵥ(T₂ - T₁)
Isentropic: Q = 0
Adiabatic: Q = 0

Steady Flow Work (Open System)

W = -∫V dP (neglecting kinetic/potential energy)

Isentropic compression:
W = [kP₁V₁/(k-1)][(P₂/P₁)⁽ᵏ⁻¹⁾/ᵏ - 1]

Polytropic compression:
W = [nP₁V₁/(n-1)][(P₂/P₁)⁽ⁿ⁻¹⁾/ⁿ - 1]

HVAC Process Applications Table

Process Type	HVAC Application	Key Equations	Typical Conditions
Isothermal	Evaporator, Condenser (phase change)	PV = C, Q = W	Saturation conditions
Isobaric	Heating coil, Cooling coil	Q = mCₚΔT	Atmospheric pressure
Isochoric	Storage tanks, Receivers	P/T = C, W = 0	Rigid vessels
Isentropic	Ideal compressor	PVᵏ = C, Q = 0	Efficiency baseline
Polytropic	Real compressor	PVⁿ = C	n = 1.2-1.35
Throttling	Expansion valve	h₁ = h₂	Pressure reduction

Process Path Representation

Thermodynamic processes are visualized on property diagrams:

P-V Diagram (Pressure-Volume):

Shows boundary work as area under curve
Isothermal: Hyperbolic curve (PV = constant)
Isobaric: Horizontal line
Isochoric: Vertical line
Isentropic: Steep curve (PVᵏ = constant)

T-s Diagram (Temperature-Entropy):

Shows heat transfer as area under curve
Isothermal: Horizontal line
Isentropic: Vertical line
Area under curve = heat transfer for reversible process

P-h Diagram (Pressure-Enthalpy):

Primary diagram for refrigeration cycle analysis
Throttling: Vertical line (constant enthalpy)
Isentropic compression: Steep curve
Isobaric heat transfer: Horizontal line

Combined Process Analysis

Real HVAC cycles combine multiple processes:

Vapor Compression Cycle:

Isentropic compression (ideal) or Polytropic (real): Compressor
Isobaric heat rejection: Condenser
Isenthalpic throttling: Expansion valve
Isobaric heat absorption: Evaporator

Air Handling Process:

Isobaric cooling: Cooling coil
Isobaric heating: Heating coil
Isobaric humidification: Spray chamber
Isobaric mixing: Return and outdoor air

Compression with Intercooling:

Polytropic compression: First stage
Isobaric cooling: Intercooler
Polytropic compression: Second stage
Improves efficiency over single-stage compression

Reversible vs. Irreversible Processes

Reversible Process:

Ideal, frictionless, quasi-static process
No entropy generation (Δs_gen = 0)
System and surroundings can return to initial state
Maximum work output or minimum work input
Serves as theoretical upper limit for real processes

Irreversible Process:

All real processes are irreversible
Entropy generation (Δs_gen > 0)
Due to friction, heat transfer across finite ΔT, mixing, throttling
Actual work greater than reversible work (compression)
Actual work less than reversible work (expansion)

Isentropic Efficiency Accounts for Irreversibilities:

Compressor: ηc = W_isentropic/W_actual = 0.70-0.85
Turbine: ηt = W_actual/W_isentropic = 0.75-0.90

Components

Isobaric Constant Pressure
Isochoric Constant Volume
Isothermal Constant Temperature
Isentropic Reversible Adiabatic
Polytropic Pvn Constant
Throttling Isenthalpic
Adiabatic No Heat Transfer
Reversible Processes
Irreversible Processes