What Is Ton of Refrigeration and COP? Definitions & Formulas

A ton of refrigeration (TR) is a unit of cooling capacity equal to the rate of heat removal needed to freeze one short ton (2000 lb) of water at 0 °C into ice in 24 hours — about 3.517 kW (12,000 BTU/h). The coefficient of performance (COP) is the dimensionless ratio of useful cooling (or heating) effect to the work input that drives the cycle. In short, TR tells you how much heat a machine moves, while COP tells you how efficiently it moves that heat per unit of energy supplied.

What is a ton of refrigeration (TR)?

The “ton” is historical: it comes from the cooling effect of melting one ton of ice over a day. The latent heat of fusion of ice is roughly 334 kJ/kg (144 BTU/lb), and working through the arithmetic for 2000 lb melted in 24 hours gives the standard value.

• 1 TR = 3.517 kW (often rounded to 3.5 kW)
• 1 TR = 12,000 BTU/h = 200 BTU/min
• 1 TR = 3024 kcal/h (approximately 50.4 kcal/min)

So a “3 TR air conditioner” removes heat at about 10.5 kW. TR is a measure of capacity (a rate of heat transfer), not of efficiency — two 3 TR units can consume very different amounts of electrical power.

What is the refrigerating effect?

The refrigerating effect (RE) is the heat absorbed by the refrigerant in the evaporator per unit mass, i.e. the useful cooling delivered. On a per-kilogram basis it equals the enthalpy rise across the evaporator:

RE = h₁ − h₄  (kJ/kg)

where h₁ is the refrigerant enthalpy leaving the evaporator and h₄ is the enthalpy entering it. The total cooling capacity is then the mass flow rate multiplied by RE:

Q̇_L = ṁ × (h₁ − h₄)  (kW)

Capacity in tons is simply Q̇_L divided by 3.517 kW/TR.

What is COP and how is it calculated?

COP compares the desired output of the cycle to the work that must be paid for. For a vapour-compression system the compressor work per unit mass is W = h₂ − h₁, so:

• Cooling (refrigerator): COP_R = Q_L / W = (h₁ − h₄) / (h₂ − h₁)
• Heating (heat pump): COP_HP = Q_H / W = (h₂ − h₃) / (h₂ − h₁)
• Relationship: COP_HP = COP_R + 1 (same machine, ideal accounting)

COP is dimensionless because numerator and denominator share the same energy units. A typical real refrigerator returns a COP of roughly 2 to 4, meaning 2 to 4 units of heat are moved for every unit of work supplied. The theoretical upper limit for given source and sink temperatures is the Carnot COP:

COP_Carnot = T_L / (T_H − T_L)  (temperatures in kelvin)

Ton of refrigeration vs COP at a glance

How are TR and COP related?

They describe different things but connect through compressor power. If a plant delivers a cooling capacity of N tons, the cooling load is Q_L = 3.517 × N (kW), and the electrical/shaft input follows from the measured COP:

Work input W = Q_L / COP_R

For example, a 2 TR unit (Q_L = 7.034 kW) running at COP 3.5 needs about 2.0 kW of compressor work. Raising COP lowers running cost for the same tonnage — which is exactly the trade-off students explore on a test rig.

Worked example

• Refrigerant mass flow: ṁ = 0.05 kg/s
• Evaporator: h₁ = 400 kJ/kg, h₄ = 250 kJ/kg → RE = 150 kJ/kg
• Compressor exit: h₂ = 430 kJ/kg → W = 30 kJ/kg

Cooling capacity Q_L = 0.05 × 150 = 7.5 kW, equal to 7.5 ÷ 3.517 ≈ 2.13 TR. COP_R = 150 ÷ 30 = 5.0. (Values are illustrative.)

Selection criteria for a refrigeration test rig

When choosing equipment to teach TR and COP, engineering departments typically weigh:

• Instrumentation: calibrated pressure gauges and temperature sensors at all four cycle points (compressor inlet/outlet, condenser outlet, evaporator inlet) so enthalpies can be read from a p-h chart.
• Energy metering: an energy meter or wattmeter for true compressor input, plus a means to measure cooling load (e.g. calorimeter, water flow and temperature rise, or an energy meter on the evaporator load).
• Refrigerant and safety: a non-flammable refrigerant, relief protection, and a clearly labelled charging port.
• Cutaway/transparent options: visible components help students connect the hardware to the cycle.
• Manuals and SOPs: a lab manual with sample readings and a p-h chart for the charged refrigerant.
• Build and standards: robust frame, quality compressor, and certified manufacture for procurement and audit.

What to ask a supplier (checklist)

• Which refrigerant is the rig charged with, and is a matching p-h chart supplied?
• Are all four state-point temperature and pressure measurements provided as standard?
• How is cooling load measured — calorimeter, electrical heater load, or water-flow method?
• Is a calibrated energy meter included for compressor input power?
• What is the rated cooling capacity (in TR/kW) and expected COP range?
• Does it ship with a lab manual, sample observation table, and wiring diagram?
• What warranty, spare-parts, and installation/commissioning support are offered?
• Are certifications (ISO 9001:2015, CE) and a CIF export quotation available?

How TR and COP are shown and measured in a teaching lab

On a refrigeration test rig, students record pressures and temperatures at the four cycle points and plot the cycle on a pressure–enthalpy (p-h) diagram for the charged refrigerant. Enthalpy differences give the refrigerating effect and compressor work per kg; multiplying RE by the measured mass flow yields cooling capacity, which is divided by 3.517 kW to express it in tons. The energy meter gives actual compressor input, so the experimental COP can be compared against the ideal cycle and the Carnot limit — making the abstract definitions tangible.

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Frequently Asked Questions

How many kW is one ton of refrigeration?

One ton of refrigeration equals 3.517 kW, which is also 12,000 BTU/h or about 3024 kcal/h. It represents the rate of heat removal needed to freeze one short ton of water at 0 degrees C into ice over 24 hours.

What is the difference between TR and COP?

TR measures cooling capacity (the rate at which heat is removed) and has units of kW or BTU/h. COP measures efficiency and is a dimensionless ratio of useful cooling effect to work input. TR tells you how much heat is moved; COP tells you how efficiently it is moved.

What is the formula for COP of a refrigerator?

For a vapour-compression refrigerator, COP_R = Q_L / W = (h1 – h4) / (h2 – h1), where h1-h4 is the refrigerating effect across the evaporator and h2-h1 is the compressor work per unit mass. The result is dimensionless.

What is the relationship between COP of a heat pump and a refrigerator?

For the same machine, COP_HP = COP_R + 1. The heat pump counts the heat rejected at the condenser as useful output, while the refrigerator counts the heat absorbed at the evaporator, and the two differ by the work input term.

How is COP measured in a refrigeration lab?

Students record pressures and temperatures at the four cycle points, read enthalpies from a p-h chart to compute the refrigerating effect and compressor work, and use an energy meter for actual input power. Experimental COP is the cooling capacity divided by the measured compressor input.

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