The Second Law and Efficiency
Heat Pumps

As previously stated, the efficiency of an energy transfer is defined as the amount of usable energy out of a transfer divided by the amount of energy that went into it.  In our homes, this is very important, since we are usually paying for the energy that goes into the transfer.  For example, the average incandescent lightbulb is only about 5% efficient while the average fluorescent light bulb is 20% efficient.  This means that you are paying four times more to run an incandescent light than you are to run a fluorescent light because you are using four times the amount of energy in using it. Of course, the fact that fluorescent light bulbs cost more than incandescent light bulbs might be a reason why you do not change to this type of lighting for your home.

The Second Law of Thermodynamics implies that the efficiency of any energy transfer is always less than 100%.  However, we do need to point out that, in the home energy arena, some people will discuss devices that sound like they are better than 100% efficient.  Specifically, in the refrigeration and air conditioning industries, people discuss energy efficiency ratios (the amount of energy transferred by a unit divided by the total amount of electrical energy input) that are sometimes as high as 500%.  Are these devices violating the Second Law?  The answer is "No."  Air conditioners and refrigerators are examples of heat pumps.  These are devices that use energy in order to transfer heat from hot to cold.  As you can see from the diagram at the right, these devices have two inputs of energy: work (W) that is supplied to the heat pump (usually electricity that is supplying a compressor) and heat (Q_c) that is withdrawn from the cold reservoir (ex. the inside of the refrigerator has heat removed).  Therefore, if we only look at the ratio of heat put into the hot reservoir to the work that we input (Q_H/W) or the ratio of heat removed from the cold reservoir to the work that we input (Q_C/W), we might get an answer that is more than 100%.  However, this is not the true efficiency of energy transfer, which would be defined as Q_H/(W+Q_C).

If this is true, why do even talk about energy efficiency ratios?  We talk about them because they are a measure of how much energy is transferred for each unit of energy that cost money.  As an example, let us look at an air conditioner.  A good central air conditioner system will have an energy efficiency ratio (Q_C/W) of about 2.5-3.0.  This means that it will remove about 2.5-3.0 units of heat from your home for each unit of electrical energy that gets charged to you.  While you are not violating the Second Law of Thermodynamics, you are getting more bang for your buck since you are not charged for how much heat you put into the hot reservoir. It is this principle that is the reason why some people install heat pump heaters in their homes. These devices are equivalent to an air conditioner working in reverse. They remove heat from the cold air outside the home in winter and transfer it to the warm insides of the home by using electrical energy. The energy efficiency ratio for them (Q_H/W) depends a great deal on how cold the air is outside. For this region of Georgia, a good heat pump heater will have an energy efficiency ration of between 2 and 3, which means that you get 2-3 times more heat put into your home than what you paid for in electrical energy. If you use natural gas to heat your home, which has an efficiency of about 65%-70%, you will be getting less heat input into your home than what you pay for in natural gas energy. However, depending upon the current price of electricity and natural gas, you might find either one as the cheaper alternative.