1.22 Efficiency

• The efficiency of a system is a measure of how well energy is transferred in a system
• Efficiency is defined as:

The ratio of the useful power or energy transfer output from a system to its total power or energy transfer 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
• Determining which type of energy is useful or wasted depends on the system
  • When electrical energy is converted to light in a lightbulb, the light energy is useful and the heat energy produced is wasted
  • When electrical energy is converted to heat for a heater, the heat energy is useful and the sound energy produced is wasted

• Efficiency can be given as a ratio (between 0 and 1) or a percentage (between 0 and 100%)
• Since efficiency is a ratio, it has no units

• Calculate energy efficiency and power efficiency in the same way, using one of the following equations;

• The energy can be of any form e.g. gravitational potential energy, kinetic energy

• Where power is defined as the energy transferred per unit of time

Step 1: Write down the efficiency equation 

Step 2: Rearrange for the power input  

Step 3: Calculate the power output

• • The power output is equal to energy ÷ time
  • The electric motor transferred electric energy into gravitational potential energy to lift the load

Gravitational potential energy = mgh = 7.2 × 9.81 × 5 = 353.16 J

Power = 353.16 ÷ 3 = 117.72 W

Step 4: Substitute values into power input equation 

Step 1: Identify the energy conversions and write them in an equation

• • The kinetic energy of the moving water is converted to gravitational potential energy as it is lifted
  • The equation should be that;

   → 

Step 2: Include the efficiency in the equation

• • Efficiency = 20% meaning 20% of the kinetic energy is converted;

Step 3: Substitute in the values and calculate

m = 7.284

Step 4: Write the answer with the correct significant figures and units

• • Mass of water lifted, m = 7.3 kg (2 s.f.)