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Efficiency compares useful output power with supplied power across the same system boundary.
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Formula
η dimensionless; P in W
| Symbol | Meaning | Unit |
|---|---|---|
| Power efficiency | dimensionless | |
| Pout | Useful output power at the stated boundary | W |
| Input power at the same boundary | W |
\eta=\frac{P_{out}}{P_{in}}For a passive machine in steady operation, 0≤η≤1 when input and useful output are consistently defined. Energy may leave as heat, sound or leakage. Transient storage requires an energy balance over an interval; do not mix electrical, thermal and mechanical boundaries.
For a passive machine in steady operation, 0≤η≤1 when input and useful output are consistently defined. Energy may leave as heat, sound or leakage. Transient storage requires an energy balance over an interval; do not mix electrical, thermal and mechanical boundaries.
Efficiency compares useful output power with supplied power across the same system boundary.
Base equation for the target quantity
Preserve signs, boundary conditions and units when rearranging.
Work through the numerical example for “Machine efficiency” and check its unit and magnitude.
A motor taking 2.0 kW electrically and delivering 1.6 kW at the shaft has η=0.80.
Substituting a related quantity that shares the same symbol.
Use variable definitions and check: η dimensionless; P in W.
Formula cluster
Efficiency compares useful output power with supplied power across the same system boundary.
A motor taking 2.0 kW electrically and delivering 1.6 kW at the shaft has η=0.80.
Compare losses and useful output of energy converters.
Here is how to work through a typical Machine efficiency (η = Pout/Pin) task step by step:
Task
Work through the numerical example for “Machine efficiency” and check its unit and magnitude.
Solution path
A motor taking 2.0 kW electrically and delivering 1.6 kW at the shaft has η=0.80.
A passive converter cannot deliver more useful power than it receives indefinitely without releasing stored energy. Values above one usually indicate mismatched boundaries, measurement error or different time bases. Define the system boundary and compare input and useful output over the same operating interval. Application: Compare losses and useful output of energy converters. The numerical example A motor taking 2.0 kW electrically and delivering 1.6 kW at the shaft has η=0.80 anchors the idea in a concrete measurement case. The corresponding units are η dimensionless; P in W. A motor taking 2.0 kW electrically and delivering 1.6 kW at the shaft has η=0.80. This checks that the reference quantities are compatible.
The ratio is formally similar, but useful output must match the process. Heat quality and temperature can matter thermodynamically; electrical and mechanical power have different boundaries. State the system and useful output for a meaningful comparison. Define the system boundary and compare input and useful output over the same operating interval. The corresponding units are η dimensionless; P in W. A motor taking 2.0 kW electrically and delivering 1.6 kW at the shaft has η=0.80. This checks that the reference quantities are compatible.
Measure supplied power and useful output at the stated boundary. Pin−Pout is loss power in steady operation if storage does not change. Heat, sound, friction and leakage are common loss paths. Define the system boundary and compare input and useful output over the same operating interval. Scope: For a passive machine in steady operation, 0≤η≤1 when input and useful output are consistently defined. Energy may leave as heat, sound or leakage. Transient storage requires an energy balance over an interval; do not mix electrical, thermal and mechanical boundaries. A practical application is Compare losses and useful output of energy converters.
Write the quantity and unit from the variable list next to every value: η dimensionless; P in W. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example A motor taking 2.0 kW electrically and delivering 1.6 kW at the shaft has η=0.80. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. Define the system boundary and compare input and useful output over the same operating interval.
The background states this starting condition: For a passive machine in steady operation, 0≤η≤1 when input and useful output are consistently defined. Energy may. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. Define the system boundary and compare input and useful output over the same operating interval.
Quanta exam set
Curated exam set for "Machine efficiency":
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Which formula describes Machine efficiency?
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How do you rearrange Machine efficiency for Base equation for the target quantity?
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Which common mistake happens with Machine efficiency?
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