9.3 BHP/ton, Isentropic Efficiency, and Theoretical Discharge Temperature
Key Takeaways
- BHP/ton is shaft horsepower divided by tons; lower is better. Input kW/ton uses measured electrical input divided by plant tons, not nameplate horsepower.
- Three-phase input kW = √3 × V_line × I × PF / 1000; multiply BHP by 0.746 for shaft kW, and divide by motor efficiency to go from shaft kW to input kW.
- Compression ratio is discharge pressure divided by suction pressure in psia (psig + 14.7 unless another barometer is given), never a ratio of gauge readings.
- Isentropic efficiency is (h2s − h1) / (h2 − h1), so actual discharge enthalpy is higher than isentropic; actual discharge temperature above the theoretical chart—read on the correct PSIG or PSIA scale—points to high ratio, high suction superheat, inefficient compression, or oil-cooler problems.
9.3 BHP/ton, Isentropic Efficiency, and Theoretical Discharge Temperature
Tons without work are a trophy. BHP/ton and kW/ton are how CIRO expects a supervisor to judge whether those tons are cheap or expensive. Discharge temperature is the quality check on the compression process: compare actual discharge temperature with the theoretical value from the on-screen chart, using the PSIG or PSIA scale that matches the pressures you have.
BHP/ton — lower is better
BHP/ton = brake horsepower / tons of refrigeration.
It is shaft work per unit of cooling. Lower BHP/ton is better. Related electrical metrics:
- Shaft kW/ton = BHP/ton × 0.746
- Input kW/ton = (BHP/ton × 0.746) / η_motor
- Input kW/ton = (measured input kW) / tons
A plant at 1.2 BHP/ton is healthier than the same plant at 2.0 BHP/ton. Nameplate HP is not BHP/ton. A 300 HP motor running at 210 shaft horsepower on 150 tons is 1.40 BHP/ton, not 300/150 = 2.0.
CIRO screens: amps, volts, PF, efficiency → input kW
Three-phase input power:
kW_in = √3 × V_line × I × PF / 1000
Use line-to-line volts, the average of three line currents if they are close, and the power factor on the screen or meter. Then:
kW/ton = kW_in / tons
Tons must come from plant data—an engine-room screen, a heat balance, or a known production load—not from compressor nameplate horsepower.
Worked screen. 480 V, 300 A average, PF 0.86, motor efficiency 93%. The evaporator/production screen shows 160 tons. (These are the same family of electrical figures CIRO sample screens use for a large screw: 480 VAC, PF about 0.86, efficiency about 93%. The amps and tons here are a teaching point, not a copied exam stem.)
kW_in = 1.732 × 480 × 300 × 0.86 / 1000
1.732 × 480 = 831.4
831.4 × 300 = 249,420
249,420 × 0.86 = 214,501
kW_in = 214.5 kW
kW/ton = 214.5 / 160 = 1.34 kW/ton
Shaft kW = 214.5 × 0.93 = 199.5 kW
BHP = 199.5 / 0.746 ≈ 267 HP — not 300 HP
BHP/ton = 267 / 160 = 1.67 BHP/ton
If someone blindly uses the 300 HP nameplate: false BHP/ton = 300 / 160 = 1.88, and any COP built on 300 HP is fiction. The motor is not at nameplate shaft load. Measure.
Same electrical input at only 120 tons (iced coils, starved DX, high suction superheat killing NRE): kW/ton = 214.5 / 120 = 1.79 kW/ton. The ammeter did not have to look worse for the plant to get worse—tons fell.
Compression ratio in psia
Compression ratio CR = P_discharge / P_suction, both absolute.
psia = psig + 14.7 (use the stem's barometer if one is given; otherwise 14.7 psi).
Worked example. Suction 20 psig, discharge 165 psig.
P_suc = 20 + 14.7 = 34.7 psia
P_dis = 165 + 14.7 = 179.7 psia
CR = 179.7 / 34.7 = 5.18
The trap: 165 / 20 = 8.25. That ratio is meaningless. At low suction the gauge-pressure error is worse. A −20°F freezer at 3.6 psig (18.3 psia) discharging at 165 psig (179.7 psia) has CR = 179.7 / 18.3 = 9.82, not 165 / 3.6 ≈ 46. High CR is why discharge temperature soars and why two-stage compression exists. This section only requires you to compute CR on an absolute basis.
Isentropic efficiency
Isentropic compression is the ideal reversible adiabatic path: entropy does not rise. On the P-h diagram it is a jump from suction pressure to discharge pressure along a constant-s line. The enthalpy at that ideal discharge state is h2s. You read h2s from the on-screen P-h diagram or from superheat tables at constant entropy—not by guessing.
Isentropic efficiency η_is = isentropic work / actual work = (h2s − h1) / (h2 − h1)
Actual discharge enthalpy h2 is higher than h2s. The extra enthalpy is wasted work: friction, leakage, non-ideal oil mixing, and irreversibility. That extra enthalpy also means a hotter discharge unless an oil cooler or liquid injection removes heat.
Worked example (read your screen for the live numbers; these values illustrate the arithmetic):
- h1 = 610 Btu/lb (suction vapor, slightly superheated)
- h2s = 738 Btu/lb (isentropic to the actual discharge pressure)
- Measured discharge state: h2 = 775 Btu/lb
Isentropic work = 738 − 610 = 128 Btu/lb
Actual work = 775 − 610 = 165 Btu/lb
η_is = 128 / 165 = 0.776 → 77.6%
Mass flow from Section 9.1 at 100 tons and NRE ≈ 456 Btu/lb was 2,633 lb/h. Actual compressor heat input:
W = 2,633 lb/h × 165 Btu/lb = 434,445 Btu/h → 434,445 / 2,545 ≈ 171 BHP → 1.71 BHP/ton
If the same pressures were isentropic:
W_s = 2,633 × 128 = 337,024 Btu/h → 132 BHP → 1.32 BHP/ton
The ~39 BHP gap is inefficiency you feel as heat: higher discharge temperature, higher oil-cooler load, higher condenser load. Never invert the ratio. Actual work over isentropic work is greater than 1 and is not efficiency.
Theoretical discharge temperature charts
CIRO provides theoretical discharge temperature charts. Axes are commonly suction pressure versus discharge temperature with families of discharge-pressure curves. Printed scales may be PSIG and PSIA. Read the scale that matches the numbers you have. Plotting 34.7 on a PSIG axis, or 20 on a PSIA axis, invents a temperature.
The chart assumes a defined suction state—typically dry saturated vapor entering the compressor. If your suction is superheated, actual discharge temperature runs higher than the saturated-suction chart even if compression is otherwise healthy. If the compressor is oil-injected, bulk discharge temperature is pulled down by oil, so a screw can run cooler than a dry reciprocating theoretical curve and still be inefficient. Compare like with like: same machine type, same suction-superheat basis.
How to use the chart on a round
- Convert suction and discharge to the chart's pressure unit (psia or psig).
- Read theoretical T_dis.
- Measure actual discharge temperature at the plant's KPI location.
- Interpret the difference, not the absolute number in isolation.
| Observation | Typical meaning |
|---|---|
| Actual ≈ theoretical (reciprocating, dry suction) | Compression near the chart basis; ratio and superheat are as assumed |
| Actual well above theoretical | High compression ratio, high suction superheat, inefficient compression (wear, leaking discharge valves), or a dirty / starved oil cooler leaving compression heat in the gas |
| Actual below a dry-gas theoretical curve on a screw | Often oil cooling doing its job—confirm oil temperature and thermosiphon flow before celebrating |
| Sudden rise versus last week's gap | Look for lift (head pressure), noncondensables, lost oil cooling, or suction superheat from a starved evaporator |
Excess discharge temperature is a diagnosis, not a personality trait of ammonia. Ammonia already runs a hot isentropic discharge compared with many halocarbons. The question is whether you are hotter than the chart at this CR.
Putting the metrics on one machine
A 180-ton plant, suction 15.7 psig (0°F, 30.4 psia), discharge 151.7 psig (85°F, 166.4 psia):
CR = 166.4 / 30.4 = 5.47 (absolute pressures from the saturation table, already in psia)
Screen: 480 V, 310 A, PF 0.86, η = 0.93.
kW_in = 1.732 × 480 × 310 × 0.86 / 1000 = 221.7 kW
kW/ton = 221.7 / 180 = 1.23 kW/ton
BHP = (221.7 × 0.93) / 0.746 ≈ 276 HP → 1.53 BHP/ton
COP_shaft = 12,000 / (1.53 × 2,545) = 12,000 / 3,894 ≈ 3.08
Heat rejection ratio ≈ 1 + 1/3.08 = 1.32
If the theoretical discharge chart at this CR and saturated 0°F suction reads about 220°F and you measure 255°F on a reciprocating machine, you have ~35°F of excess: chase superheat, valve condition, and whether the condenser is actually at 85°F saturation. If the same 255°F appears on a thermosiphon-cooled screw, read oil supply temperature before you condemn the rotors—the gas may be fine while the oil cooler is the problem, or the opposite.
Exam traps
- Compression ratio in psig.
- Nameplate HP / nameplate tons as BHP/ton.
- η_is written upside down as actual work over isentropic work.
- Ignoring chart PSIG versus PSIA scales.
- Treating high discharge temperature as "normal for ammonia" without a theoretical comparison.
- Mixing input kW/ton into a shaft COP without stating which work you used.
Isentropic compressor efficiency is which ratio?
A 480 V three-phase compressor motor draws 300 A at PF 0.86. The plant is making 160 tons. What is input kW/ton? Use √3 ≈ 1.732.
Suction pressure is 20 psig and discharge pressure is 165 psig. What is the compression ratio?
After you plot suction and discharge on the correct PSIG or PSIA scale, actual discharge temperature is well above the theoretical chart value. What does that excess most often indicate?