The Relationship Between Energy, Power, and Efficiency


Efficiency deals with the utilization of energy in a system. Energy, the capacity for doing work, can take many forms.  In our studies of wastewater treatment we have encountered several types of energy - electricity and the compression of air are just some examples.  

We are most familiar with fuels as a form of energy.  In a furnace, fuel oil is burned to produce heat.  If all of the fuel oil is consumed to provide usable heat, then the furnace would be 100% efficient.

But no furnace is 100% efficient.  Instead, some of the heat is lost through the chimney and some of the fuel in the furnace remains unburned.  As a result, a furnace is only 80 to 85% efficient.  

The Relationship Between Energy and Efficiency

Efficiency is closely related to energy, using the following formula:

This formula is very similar to the formula used for the efficiency of addition.  The pounds of meat gained by the animal can be thought of as the energy produced while the pounds of grain fed to the animal can be thought of as the energy supplied.  

On first glance, the formula above may seem to be different from the formula used for the efficiency of removal.  But you can think of the energy produced as a change in energy between the initial energy and the final energy.  So the formula for the efficiency of removal is just another version of the general formula given in this section.  


Power is also related to energy and efficiency.  Power is the way or system with which energy is harnessed.  A cow, a ball at the top of a hill, and even a leaf are all full of energy, but they are not forms of power because the energy they contain is hard for us to use.  The most familiar form of power we use is electricity, which harnesses the energy from a variety of sources (petroleum, coal, water, wind, sunlight, etc.)  In addition to electrical power, there are four other power systems: mechanical, heat, light, and fluid.

Greater power will increase the rate at which energy can be used.  In the case of a car, this increases the speed of the car - a car with a 200 horsepower motor has twice the power of a car with a 100 horsepower motor, so the 200 horsepower car runs faster, performing the same job at a faster rate.  

The Relationship Between Power and Efficiency

As the power and rate increase, energy is utilized less effectively, so the efficiency drops.  To illustrate this principle, let's consider the situation shown below.  Water is transferred from the college downhill to the greenhouse below:

If the water is allowed to flow through a 3/4 inch line throughout the day, then the pull of gravity would be all the energy which would be required to accomplish the task.  This is a power of 0, which makes the efficiency 100%.  

But if the same amount of water was supplied in 5 minutes through the same size line and over the same distance, a 5,000 horsepower pump would be required to accomplish the task.  This is a much greater requirement for power and energy as a result of the increased rate, so the efficiency is much less.  Thus, the faster a job is performed, the less efficient a system becomes in the transfer of energy and the higher the monetary cost is.