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ASPhysicsCIERevision Notes5. Work, Energy & Power5.1 Energy: Conservation, Work, Power & Efficiency5.1.3 Efficiency

Efficiency (CIE AS Physics)

Revision Note

Katie M

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Katie M

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Efficiency of a System

  • The efficiency of a system is the ratio of the useful energy output from the system to the total energy input
    • If a system has high efficiency, this means most of the energy transferred is useful
    • If a system has low efficiency, this means most of the energy transferred is wasted

  • Multiplying this ratio by 100 gives the efficiency as a percentage
  • The efficiency is calculated using the equation:

Efficiency equation, downloadable AS & A Level Physics revision notes

Efficiency equation in terms of energy

  • Efficiency can also be written in terms of power (the energy per second):

Efficiency equation 2, downloadable AS & A Level Physics revision notes

Efficiency equation in terms of power

Worked example

power-output-q

A. fraction numerator eta P subscript i n end subscript over denominator P subscript l o s t end subscript end fraction     B. fraction numerator negative eta P subscript l o s t end subscript over denominator eta space minus space 1 end fraction     C. eta P subscript l o s t end subscript     D. negative eta P subscript l o s t end subscript open parentheses eta space minus space 1 close parentheses

WE - Efficiency of a system answer image, downloadable AS & A Level Physics revision notes

Examiner Tip

Efficiency can be in a ratio or percentage format. If the question asks for an efficiency as a ratio, give your answer as a fraction or decimal. If the answer is required as a percentage, remember to multiply the ratio by 100 to convert it, e.g. Ratio = 0.25, Percentage = 0.25 × 100 = 25 %

Solving Problems Involving Efficiency

  • Recall the two equations for calculating efficiency are:

Efficiency equation, downloadable AS & A Level Physics revision notes

Efficiency equation 2, downloadable AS & A Level Physics revision notes

  • Which to use will depend on whether you’re given a system calculating energies or power as shown in the examples below

Worked example

The diagram shows a pump called a hydraulic ram.In one such pump, the long approach pipe holds 700 kg of water. A valve shuts when the speed of this water reaches 3.5 m s-1 and the kinetic energy of this water is used to lift a small quantity of water by a height of 12m.The efficiency of the pump is 20%.Which mass of water could be lifted 12 m?

A. 6.2 kg               B. 4.6 kg               C. 7.3 kg               D. 0.24 kg

WE - Efficiency of Hydraulic ram answer image, downloadable AS & A Level Physics revision notes

  • The pump is what converts the water’s kinetic energy into gravitational potential energy
  • Since its efficiency is 20%, you would multiply the kinetic energy by 0.2 since only 20% of the kinetic energy will be converted (not 20% of the gravitational potential energy)

Examiner Tip

Equations for kinetic and potential energies are important for these types of questions. Also, familiarise yourself with the different equations for power depending on what quantities are given.

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    Katie M

    Author: Katie M

    Expertise: Physics

    Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.