Modern Engineering Thermodynamics

15.7 Heat of Reaction 611
Then,
h P ° LHV = −393:522 + 2ð − 241:827Þ + 0 = −877:176 MJ/kgmole CH 4
and
h P ° HHV = −393:522 + 2ð −285:838Þ + 0 = −965:198 MJ/kgmole CH 4
Finally,
LHV = ðq r ° Þ LHV
= h P ° LHV − h R°= −877:176 − ð−74:873Þ
= −802:30 MJ/kgmole CH 4
and
HHV = ðq r ° Þ HHV
= h P ° HHV − h R°= −965:198 − ð−74:873Þ
= −890:33 MJ/kgmole CH 4
Note that this HHV is essentially the same as that listed in Table 15.2 for methane and that the HHV can be calculated from
the LHV using Eq. (15.12) as
HHV = LHV −
n H2O
n fuel
ðh fg
°Þ = LHV −
H2O n H2O
n fuel
ð44:00 MJ/kgmole H 2 OÞ
= −802:3 MJ/kgmole CH 4 − 2:00 kgmole H 2O
1:00 kgmole CH 4
ð44:00 MJ/kgmole H 2 OÞ
= −890:3 MJ/kgmole CH 4
Exercises
22. Use the methods of Example 15.8 to determine the higher heating value (HHV) of acetylene gas, C 2 H 2 (g).
Answer: HHV C2H2ðgÞ = −1299:6MJ=kgmole of C 2 H 2 (g).
23. Use the technique presented in Example 15.8 to determine the lower heating value (LHV) of propane gas, C 3 H 8 (g).
Answer: LHV C3H8ðgÞ = −2044:0MJ=kgmole of C 3 H 8 (g).
24. Repeat Example 15.8 for n-butane gas, C 4 H 10 (g). Answer: HHV C4H10ðgÞ = −2877:1MJ=kgmole of C 4 H 10 (g),
LHV C4H10ðgÞ = −2657:1MJ=kgmole of C 4 H 10 (g).
When the reactants or products are not at the standard reference state, then their enthalpies are determined from
Hess’s law by adding to the standard reference state enthalpies the change in enthalpy between the actual temperature
and pressure and the standard reference state temperature and pressure. Normally, we can ignore the
effect of pressure on enthalpy, so that the molar enthalpy of any compound at temperature T and pressure p is
hðT, pÞ, given by
hðT, pÞ = h f °+½hðTÞ − hðT°ÞŠ (15.14)
If the material can be considered to be an ideal gas with constant specific heats over the temperature range from
the standard reference state temperature T° to the actual temperature T, then we can write
hðT, pÞ = h°+c f p ðT − T° Þ (15.15)
Otherwise, hðTÞ − hðT°Þ must be determined from a more accurate source, such as the gas tables in Thermodynamic
Tables to accompany Modern Engineering Thermodynamics (Table C.16c). Combining Eqs. (15.8), (15.9),
(15.10), and (15.14) gives the general formula for the heat of reaction (or combustion) of a substance not at
the standard reference state as
q r = ∑
P
ðn i /n fuel
Þ h f °+hðTÞ − hðT°Þ i −∑ R
The use of Eq. (15.16) is illustrated in the following example.
ðn i /n fuel Þ h f °+hðTÞ − hðT°Þ (15.16)
i