One of the most fundamental principles used in all areas of science and engineering is the first law of thermodynamics. It states that energy cannot be created or destroyed, only changed in form.

For example, when a gallon of propane, which represents about 91,800 Btu of energy in chemical form, is combusted within a boiler, the majority of the chemical energy is converted into heat and transferred to a stream of water flowing through the boiler. This is useful heat output. Another portion of the energy contained in the propane becomes heat that leaves through the boiler’s exhaust system, and thus serves no useful purpose in heating the building. Yet another portion of the fuel energy drives chemical reactions during combustion, such as when hydrogen in the propane combines with oxygen in the air to produce water vapor.

If one were to precisely measure all the energy released from or stored within the boiler in this situation, in both useful and unusable forms, and add them up, the total would always equal the original chemical energy in the gallon of propane. Although the energy was converted to different forms within the boiler, none of it was ever destroyed.

This underlying principle of the first law of thermodynamics is sometimes stated as, “Energy in equals energy out.” This concept is often used as the basis of energy balance equations. Those equations simply imply that, under steady state operating conditions, all the energy flowing into a process must equal the total energy flowing out of that process. Heat balance equations are useful in predicting energy flows that might not be easily measured or otherwise calculated. They are also used in establishing the thermal efficiency of devices such as solar collectors, heat pumps and boilers.

The thermal efficiency of any device that converts one form of energy into heat is the ratio of the useful heat output from that device, divided by the energy input to the device. The greater this ratio, the higher the thermal efficiency of the device.

The principle of thermal efficiency also applies to a complete heating system. Here, the objective is to maximize the useful energy delivered to the heating load, per unit of energy contained in the original energy source. This objective applies to all facets of design, installation and operation of the heating system. Any design details that improve the thermal efficiency of a heating system, while also being cost effective, are generally desirable.

### The second law

When designing heating systems, especially those with renewable energy heat sources, it’s important to consider the second law of thermodynamics. Historically, this law has been stated in many ways by famous scientists such as Carnot, Kelvin and Plank. Some of these statements are highly technical, and beyond discussion in this article. However, there are several practical ways to consider the second law of thermodynamics. One of the simplest is as follows: Heat always moves from an area of higher temperature to an area of lower temperature.

Another way to think about the second law of thermodynamics involves a quantity called entropy, which is a measure of the usefulness of energy. Energy at low entropy is very useful, whereas energy at high entropy is less useful, or perhaps even useless.

The second law of thermodynamics states that the entropy of any isolated system always increases with time. In other words, all energy in the universe is continually changing from lower entropy to higher entropy, and thus becoming less useful.

Examples of energy in low entropy form are electricity and the heat available from a 2,500° F flame. Both of these energy sources are highly useful. Electricity can be used to operate a wide range of devices such as motors, heat pumps or even converted directly into heat at very high temperatures. One example of the latter is the tungsten filament in an incandescent light bulb, which converts electrical energy into heat at a temperature of about 5,400°. Heat from a 2,500° flame could heat several types of metal to their melting points. It could also be used to create steam, to heat buildings or operate a powerful steam engine. In short, both of these low entropy energy sources are highly useful in a wide range of applications.

Two examples of energy in high entropy form are the heat in air at 40°, or the heat available when an ice melts into liquid water at 32°. There can be a large quantity of heat in a large volume of 40° air, but none of that energy can be directly transferred to maintain the temperature of a room at 70°. Although many people might disagree, there can also be a large quantity of heat in ice. Every pound of water at 32° must release 144 Btu of heat to change into a pound of ice at 32°. Imagine how much heat must be released from the water at the surface of a large lake when it freezes over in winter. Even though billions of Btu of heat energy are released from the water during this process, not one of them can be directly transferred to heat a room at 70°. That’s because heat cannot directly move from an area of lower temperature to one at higher temperature. Thus, high entropy energy, although often plentiful in supply, is less useful than low entropy energy.

It’s important not to confuse the entropy of energy with the quantity of energy. There can be vast amounts of energy present in a material, but in high entropy form. The energy released as a large lake freezes in winter is an example. Similarly, the entropy of heat available from the flame of a burning match makes that energy very useful, even though the quantity of heat available is very small. A completely burned wooden match only releases about 1 Btu of heat.

From the standpoint of the second law of thermodynamics, using heat from a 2,500° flame to heat a building at 70° is poor use of the entropy of that energy (e.g., this would convert energy at relatively low entropy to much higher entropy, and therefore to a much less useful state). The low entropy energy in the 2,500° could be used to create steam, which could drive a turbine, which could spin a generator to produce electricity, which could power a heat pump or light a lamp. Such a process is routinely used in many gas-fired and coal-fired electrical generating facilities. However, this process only converts about 1/3 of the original energy in the fuel to electricity. The remaining 2/3 of the energy from the fuel becomes heat, which is often dissipated to the atmosphere using large cooling towers.

A good example of matching the entropy of energy with an application for that energy is using a heat pump to heat a building. Under certain conditions, heat pumps are capable of moving 4 to 5 units of low temperature heat from outside air or soil, into a building with an interior air temperature of about 70°, using only one unit of electrical energy in this process. Thus, one unit of low entropy electrical energy has allowed the practical use of 4 or 5 units of high entropy energy. Such a process “respects” the second law of thermodynamics.

Another example that respects the second law of thermodynamics is the use of a large surface area hydronic heat emitter, such as a floor with embedded tubing, used in combination with a renewable heat source such as solar thermal collectors or a heat pump. Both of these heat sources are more efficient at gathering renewable energy when operated at low water temperatures. Coupling either of these heat sources to a large surface area hydronic radiant panel could allow water in the range of 90° to 100° to maintain excellent comfort in a building, even on a cold winter day. By contrast, using a heat emitter with a smaller surface area could force the system to operate at an average water temperature of 130° or higher. Although this may be possible, the efficiency of both heat sources would be significantly lower under such conditions. Good design practice seeks to match high entropy energy sources such as solar heat stored in “cool” outside air, with low temperature heat emitters. The closer the temperature of the energy source is to the final temperature required for the process, the better the design from the standpoint of the second law of thermodynamics. From the standpoint of heating buildings, the lower the operating temperature of the hydronic distribution system, the better the system can use the relatively high entropy thermal energy available from the renewable energy heat sources.

It’s likely the continued refinement of modern hydronic heating technology will be more influenced by the need to use higher entropy (lower temperature) energy sources, and match them with compatible (lower temperature) heat emitters.

Entropy — like energy — is not something to be wasted.