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Unformatted text preview: Bomb calorimeter 2.3 Heating Values 29 Because the ﬁnal water temperature is close to room temperature, the water in
the combustion products is usually in liquid phase. Therefore the measurement leads
to the HHV from a constantvolume combustion process as described by Eq. 2.32:
(
HHV ¼ ÀQ0 ;v
rxn À X Ni;P À X i ! ) Â
Ã
^
Ni;R Ru T0 = Nfuel Mfuel ; i where Nfuel is the number of moles of fuel burned and Mfuel is the molecular weight
of the fuel. The negative sign in front of Q0 ;v ensures that HHV is positive. In a
rxn
bomb calorimeter, if the ﬁnal temperature of the combustion products is higher than
the reactants by only a few degrees (<10 C), the error is negligible. The amount of
heat transfer is estimated by
À Q0 ;v ¼ ðmsteel Á cp;steel þ mwater Á cp;water ÞDT ;
rxn (2.35) where DT is the temperature change of the water and the steel container.
The bomb calorimeter can also measure the enthalpy of formation of a chemical
species. For instance, to determine enthalpy of formation of H2O, we start out with
1 mol of H2 and 0.5 mol of O2. These element species have zero enthalpy of
formation; therefore
X ^0
Ni;R Dhi;R ¼ 0: i The only product is the species of interest, namely H2O. We therefore can write the
^
enthalpy of formation of H2O, Dhi0P , as
; ^
Dhi0P
; ¼ Q0 ;v
rxn þ
P Ni;P À i P ^
Ni;R Ru T0 i ¼ Ni;P ^
Q0 ;v þ DN Ru T0
rxn
Ni;P (2.36) where
DN ¼ X Ni;P À i 2.3.3 X Ni;R : i Representative HHV Values Listed in Table 2.3 are higher heating values of some common and less common fuels.
Example 2.4 A table of thermodynamic data gives the enthalpy of formation
^0
for liquid water as DhH2 OðlÞ ¼ À285.8 kJ/mol. A bomb calorimeter burning 1 mol of
H2 with O2 measures 282.0 kJ of heat transfer out of the reacted mixture. Estimate
the error of the enthalpy measurement. 30 2 Thermodynamics of Combustion Solution:
We start out with the combustion stoichiometry
H2 ðgÞ þ 0:5O2 ðgÞ ¼ H2 OðliqÞ;
DN ¼ À1:5 ðChange in moles of gas in the mixtureÞ Applying the ideal gas approximation to...
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This document was uploaded on 01/20/2014.
 Winter '14
 Physics, Energy, Heat

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