Scrutinizing Condensing Boilers With the Second Law of Thermodynamics (SLT)

“It’s amazing. Every year, we find somebody who comes up with a way of going around the second law (of Thermodynamics) and somehow convinces people who are very smart that it will work.”      MIT lecture on  Thermodynamics and & Kinetics, Spring 2008



Since the 1980s, hot water condensing boilers (CB) have aimed to improve efficiency by utilizing the heat of water vapor condensation from flue gas. Modern CB continue to be notorious for corrosion and cold weather problems [ThisIsMoney, Guardian] and need thorough (and expensive) home insulation. Still, the market share of CB grows steadily, thanks to favorable incentives and government regulations.

      The Annual Fuel Utilization Efficiency (AFUE) value for CB is estimated at 92-98%, compared to 82-86% for non-condensing boilers. “Many people today are very pleased to assert that the efficiencies of certain space-heating systems are nearly 100%. This way of thinking often projects an incorrect picture of a space-heating system” [Wall Goran]. 

            AFUE is measured based on the First Law of Thermodynamics as a ratio of utilized heat (heat from fuel combustion minus heat loss through the chimney) to supplied heat (heat from fuel combustion). However, “boiler efficiency, as commonly defined, is very misleading. These efficiencies are normally of the order of 80 to 90%, whereas the second-law efficiency of Industrial boilers is generally 30 to 45%... Two boilers with identical first-law efficiencies may be vastly different from a second-law viewpoint; e.g., one generating steam at a high pressure (and therefore temperature) will be much more efficient than one delivering steam at a low p (and T)” [Energy Engineering]

      Second-law efficiency is also known as exergy efficiency. A quick and simple explanation of the concept of exergy can be found here. Exergy deals with the energy quality and the potential to produce useful work from the viewpoint of the SLT. One Btu of heat has different potential for useful work at high and low temperatures, just as U.S.  and Taiwan dollars have different purchasing power. Among other things, it means that maximum possible efficiency can never exceed 100%. It is not uncommon for members of environmentalist groups to circumvent this law. Reports of energy efficiency levels of 104% and even 109% have raised few, if any, doubts or objections.

      The exergetic efficiency of a steam or hot water boiler can be calculated using the following general equation [Szargut Jan, eq. 2.33]:

ηB =   (ηE/α) (1- To/Tm)                                                              (1)

Where            ηB - boiler exergy efficiency,

ηE – boiler energy efficiency,

α – ratio of chemical exergy of fuel to its chemical energy (considered 1 hereafter)

To,K – ambient temperature,

Tm,K – mean thermodynamic temperature of the heated fluid during heat absorption (temperature of hot water supply).

            Normally, the operating temperature of a hot water boiler is below 180oF/82.2oC.  In a condensing boiler, this upper temperature bound is reduced to below 130oF/55oC in order to condense water from flue gas [Lehigh U, Engineering Toolbox]. The recommended temperature for water entering the condensing section (also called the boiler return temperature) is 100oF/37.8oC or lower. Assuming the typical temperature difference of 20oF throughout the hot water system, that corresponds to a 120oF temperature for the boiler’s water supply.

      For estimation, a closed system that includes a boiler, radiators, and a house at To = 63oF/17oC is assumed in equilibrium with the environment. Heat loss from a house is proportional to the temperature difference from the outside temperature and is offset by heat from the radiators at temperature Tm. In Table1.pdf, the exergetic efficiencies of a hot water boiler, a hot water condensing boiler, and a steam boiler are calculated based on typical energetic efficiency AFUE and heating media temperature. Please note that these exergetic efficiencies are maximum values that can only be achieved ideally and are independent of boiler and distribution system design.

      Exergetic analysis clearly indicates that although the AFUE of a CB is close to 100%, its relative exergetic efficiency is 39.7% less than a non-condensing boiler’s (9.4% versus 15.6% – Table 1). The estimated CB exergy efficiency falls within the data range reported in literature [Lohani -5%, Kilkis – 5%, CCS- 8%, Favrat -12%]. “This low efficiency is the result of the conversion of a high-quality fuel, natural gas, into low temperature heat.” A comparison of the typical energy and exergy flows of a CB is shown here.

      What do these numbers mean? Essentially, if the boiler must use fuel, it makes more sense to use the heating media at higher temperatures. From an exergy point of view, a steam boiler is a better option than a hot water one, but the high mass, poor control, and uneven heat distribution in old steam systems wipes out this advantage.

      This conclusion contradicts numerous reports on the energy savings achieved by CB. To clarify the discrepancy, consider the annual boiler load distribution. For illustration, DOE and CARB operational data on seasonal thermal efficiency of a CB are presented in Table2.pdf and Table3.pdf, respectively. Calculated values are shown in italics. An average room temperature of 65oF and supply water temperature are used as To and Tp, respectively.

      An exergy analysis of each data set reveals the same trend: overall efficiency is attributed to a 6-7% increase in “condensing mode energy efficiency” achieved during 31- 35% of the heating load. Omitted from the picture is that the boiler operates at a 43-47% higher exergetic efficiency in non-condensing mode (during the other 65-69% of the time). As Richard P. Feynman said, “The first principle is that you must not fool yourself, and you are the easiest person to fool.” 

      According to traditional energy analysis, condensing mode usage (along with its allegedly mighty savings) is highest at warmer outside temperatures and lower temperatures of return water. But CB account for only 2% of all boilers in sunny Italy [LEAP], presumably because of lack of government incentives. Surprisingly, in the UK, the CB percentage is close to a hundred [UK market update, p. 17], thanks to regulations and the colder, more humid weather.


        The presented exergy analysis demonstrates how and why the results of very thorough research produced erroneous conclusions. None of this is meant to reject the concept of CB in general; rather, I mean to clarify the inborn catch-22 of hot water systems. In fact, the concept can succeed in 2-pipe steam and vacuum systems, in which a significant temperature difference between the supply water vapor and liquid condensate return is achieved naturally because of a phase change in the radiators.




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Comment by Igor Zhadanovsky on November 20, 2013 at 7:41pm

Seith and Kurt:

Thanks for your comments.

Kurt’s statements sounds right but as usual, devil is in details:

Lower quality heat is easier to obtain and generally costs less. Designing your emitter system to operate using a lower quality heat source is a good thing. 

What source the low quality heat source come from? Heat pump consumes electricity (high quality energy) and, often, requires backup boiler for cold days.  Heat and power co-generation (either district or distributed) is actually the only reliable alternative which is not available everywhere.    

Parasitic losses in the distribution system are lower as well.  Heat losses in low quality distribution system are lower, but this system usually employ extensive heating area (not cheap to install) and electrical pumps (parasite losses as well).  In addition, such systems are vulnerable to power shortages; back generator is an option, not cheap though.

For each particular case, simple “napkin” calculations would help like (my favorite on TED).

The basic questions would be:

What’s the installation cost? Efficiency gain? Pay back period? Resilience? etc.

I live in a house with steam heating system (gas fuel , pilot element/no electricity dependency). Power shortage never effects on house heating, - is it worth extra dollars on fuel bill? Is it cost more then back up generator?  Is it more then possible frozen pipes repair?   

Comment by Kurt Albershardt on November 20, 2013 at 3:05pm

Hot water is a lower quality heat source than steam.  100ºF water is a lower quality heat source than 180ºF water.  Lower quality heat is easier to obtain and generally costs less.

Designing your emitter system to operate using a lower quality heat source is a good thing.  Parasitic losses in the distribution system are lower as well.

Comment by Seth Rutledge on November 20, 2013 at 2:40pm

Am I understanding this correctly: basically lower temperature water does not transfer heat as efficiently as higher temp. water; so even if theoretically you captured 100% of the energy of the fuel if the energy is the same temp. as it is outside you are not going to be warming anything? 

This certainly jives with my annoyance at the cold/lukewarm air that blows out of those high efficiency furnaces and almost make me feel colder.  

However, I wonder if there is not another side to this; say for example that I have radiant floors and walls oversized for my heat load so that I can heat my house with 100degF water from a heat storage tank.  Even though the heat exchange is lower (because of a lower temp. difference) per square foot, because the radiant area is larger then it balances out.  I don't see how in this case the lower exergy efficiency of the lower temp water would have an impact on the heating bill.  Am I understanding this correctly?

Comment by Kurt Albershardt on July 3, 2013 at 10:59am

I heartily agree that AFUE needs a major re-work. I do believe that measuring overall system efficiency (in something like BTUs per square foot per degree-day) will factor in these second law effects.   As long as we include pumping costs, it will also allow far comparison between system types without even knowing details of the particular system used.

Comment by Igor Zhadanovsky on June 8, 2013 at 10:58pm


thanks for good words about article.

It took me a while to figure out how temperatures, AFUE, energetic and exergetic efficiencies are interconnected for  heating systems. Fortunately, found very logical explanation - Szargut Jan., eq. 2.33 These basic ideas are not, actually, simple and straightforward, - it's a reason why SLT  is commonly circumvented today. I'll be glad to answer Curt's questions to the best of my knowledge.      

Comment by John M Rogers on June 8, 2013 at 1:43pm

It's hard for me to understand how impatient Curt is behaving about having a college level discussion on some simple basic ideas. Give me more conceps to let simmer in my knowledge base, please. Wonderful article

Comment by Igor Zhadanovsky on June 8, 2013 at 7:46am


1lb stone weight at 100 ft elevation is the same at 1 ft,  but has potential energy 100 times  more relative to ground level. Temperature parameter for potential energy of 1  BTU is similar to elevation for stone - it indicates how much potential energy (exergy) this BTU has relative to reference temperature.

In practical terms: one cup of hot tee will warm you up better then a gallon of tepid tee.  

You can find is a great explanation of exergy here - click on Energy & Exergy explained.

Comment by Curt Kinder on June 7, 2013 at 1:51pm

Thanks for the review of thermodynamics. Fortunately, I've already eaten a tasty lunch.

Chilly homeowners care not a wit about the work potential of heat they need to stay warm. They are interested in safety, health, comfort and efficiency, generally in that order.

The work potential of a Btu in Zanzibar or Zebulon is irrelevant. A Btu in Taiwan has the exact same heat energy as a Btu in Timbuktu, whether paid for in Drachma or Dollars.

Help us understand how Exergy, Empathy, or Philately help homeowners have a safe, healthy, comfortable, and efficient HVAC system.

Comment by Igor Zhadanovsky on June 7, 2013 at 1:35pm

The Laws of Thermodynamics

1. Energy is conserved.

2. dW ≤ dQ ≤ TdS + Sdt

[Condensed form for experts]

3. S=0 at T=0.


1. You can’t win.

2. You can’t even break even.

3. You can’t leave the game.


1. There is no free lunch.

2. The lunch will always cost more than you think.

3. You have to eat.


A quick and simple explanation of the concept of exergy can be found here. Exergy deals with the energy quality and the potential to produce useful work from the viewpoint of the SLT.

One Btu of heat has different potential for useful work at high and low temperatures, just as U.S.  and Taiwan dollars have different purchasing power.

Eventually, any home owner care about fuel bill:

Imagine "ideal" hot water condensing boiler  - AFUE close to 100% (input/ouput temperatures are 41/61oF). Your house has no heat loss and is at 61oF now; the  thermostat setting is 65oF.  

How long will it take to get the house warm to 65oF?  

Comment by Curt Kinder on June 7, 2013 at 12:21pm

So a homeowner is really better off with an 80% AFUE appliance compared with a 90+% model?

Why would any homeowner care about "Exergy"?

Let me go check my Exergy balance at my online banking and I'll get right back to you!

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