Efficiency
Efficiency is a measure of how effectively an energy transfer or transformation occurs in a system, often expressed as the ratio of useful energy output to the total energy input. The efficiency of a process or device provides insights into how well it converts the input energy into the desired output, considering losses and wastage during the conversion.
Mathematically, efficiency (η) can be calculated using the formula:
= Useful energy outputTotal energy input 100%
Efficiency is typically expressed as a percentage. A system with 100% efficiency would indicate that all the input energy is converted into useful output without any losses, which is an ideal scenario but often unattainable in real-world situations due to factors such as friction, heat dissipation, and other forms of energy dispersion.
Efficiency of Energy Transfer
Efficiency in the context of energy transfer refers to how well a system converts the input energy into useful output energy. In any energy conversion process, some energy is always lost, typically as heat, sound, or other forms of waste energy. The goal is to maximise the useful energy output while minimising the energy lost in the conversion process.
Qualitative Explanation:
Imagine you have a machine that takes in 100 units of energy. If it only produces 70 units of useful energy, the remaining 30 units are lost, often as heat. The efficiency of this machine is a measure of how effectively it converts the input energy into useful energy.
Analogies:
Money Management: If you earn $100 and save $70, the remaining $30 might be spent on unnecessary expenses. Your efficiency in saving money is 70%.
Food Energy: When you eat food, not all the energy from the food is used by your body for activities. Some of it is lost as heat. If you consume 100 calories and your body uses 75 calories for activities, the efficiency is 75%.
Solved problems:
(a) Efficiency in Terms of Energy:
Suppose a light bulb uses 100 joules (J) of electrical energy and produces 75 joules of light energy. The efficiency can be calculated as follows:
This means that 75% of the electrical energy is converted into light, while the remaining 25% is lost, primarily as heat.
(b) Efficiency in Terms of Power:
Consider an electric motor that consumes 200 watts (W) of electrical power and produces 150 watts of mechanical power. The efficiency can be calculated as follows:
This means that 75% of the electrical power is converted into mechanical power, with 25% lost, typically as heat.
Derivation of P = Fv
The power delivered to a moving object is described by the equation:
Where:
P = power in watts (W)
F = force in newtons (N)
v = velocity in metres per second (m s-1)
This equation is only relevant where a constant force moves a body at constant velocity
Power is delivered to the object by a force in order to produce an acceleration
The force must be applied in the same direction as the velocity
Derivation
Power is the rate of doing work
Work is done when a force moves an object over a distance
At a constant velocity, the distance moved by the object can be described as:
Substituting this into the work done equation gives:
And substituting this into the power equation gives:
