# Heating Values of Various Fuels

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*"standard enthalpy (heat) of combustion"*may be a misleading measure of a fuel's heating value in real conditions. Standard enthalpies are precisely defined as the heat energy absorbed or released when a process occurs at 25

^{o}C to give substances in their most stable state at that temperature. For example, for propane, water is produced as a liquid:

C

_{3}H

_{8}(

*g*) + 5 O

_{2}(

*g*) → 3 CO

_{2}(

*g*)+ 4 H

_{2}O (

*l*) Δ

*H*= –2219.2 kJ

_{m}^{[1]}(1)

But boilers are almost always operated with flue temperatures near the combustion temperature, and maintained at over 100 ^{o}C to prevent water from condensing to liquid. Since water is produced as a gas, the standard thermodynamic equation (1), does not apply. If it were formed, liquid water would dissolve acidic flue gases like HCl and SO_{2} to make acidic solutions which corrode the system. These gases are normally removed by limestone "scrubbers",^{[2]} leaving just the water vapor. The white plumes over smokestacks are water droplets forming by condensation of water vapor. They often disappear as the droplets evaporate.

The precision of our definition of *standard enthalpy* guarantees that our calculations of heat energy will be sound, but it requires that we *pay attention to* each energy cost and source. We'll see that inattention to such details has led to misinformation and confusion. Since Higher Heating Value (HHV) may be used by some air quality management authorities,^{[3]} while Lower Heating Values are used by many engineers and European power facilities, it is important to know precisely what the terms mean and which is being used. The USDA^{[4]} reports the following heating costs apparently, but not explicitly, stated to be LHVs:

Fuel |
Gross heating value |
Efficiency (%) |
Net heating value |
Fuel required for 1 million Btu of usable heat |
Average cost/unit |
Total annual fuel cost |
---|---|---|---|---|---|---|

Natural gas | 1.03 million Btu/1000 ft^{3} |
80 | 0.82 million Btu/1000 ft3 | 1,220 ft^{3} |
$7/1000 ft3 | $854 |

Propane | 91,200 Btu/gal | 79 | 72,000 Btu/gal | 13.86 gal | $1.25/gal | $1,730 |

Fuel oil #2 | 138,800 Btu/gal | 83 | 115,000 Btu/gal | 8.68 gal | $1.40/gal | $1,220 |

Seasoned firewood | 20 million Btu/cord | 77 | 15.4 million Btu/cord | 0.065 cord | $115/cord | $747 |

Electricity | 3,413 Btu/kWh | 98 | 3,340 Btu/kWh | 299 kWh | $0.08/kWh | $2,390 |

Premium wood pellets | 16.4 million Btu/ton | 83 | 13.6 million Btu/ton | 0.073 ton | $120/ton | $882 |

^{a} Based on 100 million Btu of energy for the heating season, a typical value for an average sized house.

There are many variables that affect total heating costs (furnace efficiencies, local energy costs, etc.), but one variable that can potentially be understood is the heat available from fuel combustion. Without precise definitions, even this may be obscured. To illustrate this point, let's examine what are known as the Higher Heating Value (HHV)^{[5]} and Lower Heating Value (LHV)^{[6]} are calculated for propane.

## The HHV

The standard heat of combustion of propane is

C_{3}H

_{8}(

*g*) + 5 O

_{2}(

*g*) → 3 CO

_{2}(

*g*)+ 4 H

_{2}O (

*l*) Δ

*H*= -2219.2 kJ

_{m}^{[7]}=

*= Δ*

**HHV***H*

_{1}(1)

This is the process which yields the HHV, because the fuel is burned and the combustion products are cooled to 25 ^{o}C, removing all heat resulting from the condensation of water in the process.

## The LHV

But we want the enthalpy for the reaction:

C_{3}H

_{8}(

*g*) + 5 O

_{2}(

*g*) → 3 CO

_{2}(

*g*)+ 4 H

_{2}O (

*) Δ*

**g***H*=

_{m}*= Δ*

**LHV***H*

_{2}(2)

In this case, the water is not condensed, so some of the energy is not recovered, so the Δ*H _{m}* is the Lower Heating Value. We can imagine reaction (2) occurring in two steps. First, reaction (1), then

H_{2}O(*l*) → H_{2}O(*g*) Δ*H _{m}* = 44.0 kJ (3)

_{2}O (

*l*), so we multiply equation (3) by 4, so that 4 moles of H

_{2}O (

*l*) are consumed in equation (3a):

4 H_{2}O(*l*) → 4 H_{2}O(*g*) Δ*H _{m}* = 4 x 44.0 kJ = 176.0 kJ (3a)

If we add equations (1) and (3a) as below, canceling the 4 mol H_{2}O (*l*) that are produced (appear on the right) with the 4 mol H_{2}O (*l*) which are consumed (appear on the left), we get equation (2).

C_{3}H_{8}(*g*) + 5 O_{2}(*g*) → 3 CO_{2}(*g*) + ~~4 H~~ Δ_{2}O (*l*)*H _{m}* = –2219.2 kJ (1)

~~4 H~~ → 4 H_{2}O(*l*)_{2}O(*g*) Δ*H _{m}* = 4 mol x 44.0 kJ mol

^{–1}= 176.0 kJ (3a)

————————————————————————————————————————

C_{3}H_{8}(*g*) + 5 O_{2}(*g*) → 3 CO_{2}(*g*)+ 4 H_{2}O (* g*) Δ

*H*= LHV = Δ

_{m}*H*

_{2}=–2043.2 kJ (2)

Experimentally it is found that the enthalpy change for reaction (2) is the

*sum*of the enthalpy changes for reactions (1) and (3a):

Δ*H*_{2} = –2219.2 kJ + (4 x 44.0 kJ) = –2043.2 kJ = Δ*H*_{1} + 4 x Δ*H*_{3}

This value of Δ*H _{m}* should be the Lower Heating Value. Let's see if it matches the USDA value of 91,200 BTU/gal in the table above, given that a gallon of propane is about 4.23 lb

^{[8]}

Our value is not close to the USDA LHV, but it matches the Oak Ridge National Laboratory (ORNL) value for the HHV of 84 250 BTU/gal^{[9]}.

The Higher Heating Value is the enthalpy change for reaction (1), which includes the heat released when 4 mol of gaseous water from the combustion cool to 25 ^{o}C, so its value is more negative than the LHV by four times the heat of condensation of water (–2043.2 + 4 x (–-44) = –2219.2 kJ):

H_{2}O(*g*) → H_{2}O(*l*) Δ*H _{m}* = –44 kJ (4)

Repeating the calculation for the heat liberated in equation (1) in BTU/gal, we get 91 500 BTU/gal, which is the HHV reported by ORNL. The USDA table above apparently reports the HHV, perhaps unknowingly. The variety of values found on the web for both HHV and LHV attests to the fact that much confusion can result from not being careful with the meaning and application of a *standard enthalpy*.^{[10]} Technically, the lower heating value of a fuel is defined as the amount of heat released in the combustion of the fuel to give products at 150°C.^{[11]}

## Hess' Law

In the general case it is always true that *whenever two or more chemical equations can be added algebraically to give a net reaction, their enthalpy changes may also be added to give the enthalpy change of the net reaction*.

This principle is known as **Hess' law**. If it were not true, it would be possible to think up a series of reactions in which energy would be created but which would end up with exactly the same substances we started with. This would contradict the law of conservation of energy. Hess’ law enables us to obtain Δ*H _{m}* values for reactions which cannot be carried out experimentally, as the next example shows.

## Example 1

Acetylene (C_{2}H_{2}) cannot be prepared directly from its elements according to the equation

*s*) + H

_{2}(

*g*) → C

_{2}H

_{2}(

*g*) (1) Calculate Δ

*H*for this reaction from the following thermochemical equations, all of which can be determined experimentally: C(

_{m}*s*) + O

_{2}(

*g*) → CO

_{2}(

*g*) Δ

*H*= –393.5 kJ (2

_{m}*a*) H

_{2}(

*g*) + ½O

_{2}(

*g*) → H

_{2}O(

*l*) Δ

*H*= –285.8 kJ (2

_{m}*b*) C

_{2}H

_{2}(

*g*) + O

_{2}(

*g*) → 2CO

_{2}(

*g*) + H

_{2}O(

*l*) Δ

*H*= –1299.8 kJ (2

_{m}*c*)

**Solution** We use the following strategy to manipulate the three experimental equations so that when added they yield Eq. (1):

**a)** Since Eq. (1) has 2 mol C on the left, we multiply Eq. (2*a*) by 2.

**b)** Since Eq. (1) has *1* mol H_{2} on the left, we leave Eq. (2b) unchanged.

**c) **Since Eq. (1) has *1* mol C_{2}H_{2} on the *right*, whereas there is *1* mol C_{2}H_{2} on the *left* of Eq. (2c) we write Eq. (2c) in reverse.

*s*) + H

_{2}(

*g*) → C

_{2}H

_{2}(

*g*) Δ

*H*= 227.0 kJ

_{m}

## References
- ↑ http://webbook.nist.gov/cgi/cbook.cg...k=1#Thermo-Gas
- ↑ http://en.wikipedia.org/wiki/Flue-gas_desulfurization
- ↑ http://en.wikipedia.org/wiki/Talk:Heat_of_combustion
- ↑ http://www.fpl.fs.fed.us/documnts/te...calculator.pdf
- ↑ http://en.wikipedia.org/wiki/Lower_heating_value
- ↑ http://en.wikipedia.org/wiki/Lower_heating_value
- ↑ http://webbook.nist.gov/cgi/cbook.cg...k=1#Thermo-Gas
- ↑ The density of liquid propane at room temperature is variously reported as 0.498 g/mL (4.1 lb/gal) at 25
^{o}C also here or 4.23 lb/gal to 5.1 lb/gal at 60 ^{o}F. Part of the problem is that the density is pressure dependent, and the tank (vapor) pressure of propane changes significantly with temperature. It is about 883 kPa (~8 Atm) at 27 ^{o}C
- ↑ http://cta.ornl.gov/bedb/appendix_a/...ious_Fuels.xls
- ↑ Neither the LHV or HHV correct for the difference between the enthalpy of the reaction at 25
^{o}C and the enthalpy change at the actual compustion temperature, which depends on the heat capacities of the reactants and products
- ↑ http://cta.ornl.gov/bedb/appendix_a/...ious_Fuels.xls

### Contributors
Ed Vitz (Kutztown University), John W. Moore (UW-Madison), Justin Shorb (Hope College), Xavier Prat-Resina (University of Minnesota Rochester), Tim Wendorff, and Adam Hahn.

^{o}C also here or 4.23 lb/gal to 5.1 lb/gal at 60^{o}F. Part of the problem is that the density is pressure dependent, and the tank (vapor) pressure of propane changes significantly with temperature. It is about 883 kPa (~8 Atm) at 27^{o}C^{o}C and the enthalpy change at the actual compustion temperature, which depends on the heat capacities of the reactants and products### Contributors
Ed Vitz (Kutztown University), John W. Moore (UW-Madison), Justin Shorb (Hope College), Xavier Prat-Resina (University of Minnesota Rochester), Tim Wendorff, and Adam Hahn.

Ed Vitz (Kutztown University), John W. Moore (UW-Madison), Justin Shorb (Hope College), Xavier Prat-Resina (University of Minnesota Rochester), Tim Wendorff, and Adam Hahn.