FUELS AND COMBUSTION 497dharm
\M-therm\Th11-1.pm5partial pressures of the remaining constituents is constant. The vapour then occupies the same
proportion of the total volume at each measurement. Hence the vapour does not affect the result of
the analysis.
Note. Quantitatively the dry product analysis can be used to calculate A/F ratio. This method of obtaining
the A/F ratio is not so reliable as direct measurement of air consumption and fuel consumption of the engine. More
caution is required when analysing the products of consumption of a solid fuel since some of the products do not
appear in the flue gases (e.g. ash and unburnt carbon). The residual solid must be analysed as well in order to
determine the carbon content, if any. With an engine using petrol or diesel fuel the exhaust may include unburnt
particles of carbon and this quantity will not appear in the analysis. The exhaust from internal combustion engines
may contain also some CH 4 and H 2 due to incomplete combustion. Another piece of equipment called the Heldane
apparatus measures the CH 4 content as well as CO 2 , O 2 and CO.
11.16. INTERNAL ENERGY AND ENTHALPY OF FORMATION
The first law of thermodynamics can be applied to any system. Non-flow and steady-flow
energy equations deducted from this law must be applicable to systems undergoing combustion
processes.
It has been proved experimentally that the energy released, when a unit mass of a fuel
undergoes complete combustion, depends on the temperature at which the process is carried out.
Thus such quantities quoted are related to temperature. Now it will be shown that if the energy
released by a fuel at one temperature is known then it can be calculated at other temperatures.
The process of combustion is defined as taking place from reactants at a state identified by
the reference temperature T 0 and another property, either pressure or volume, to products at the
same state.
Let UR 0 = Internal energy of the reactants (which is a mixture of fuel and air) at T 0 ,
UP 0 = Internal energy of products of combustion at T 0 ,
UR 1 = Internal energy of reactants at temperature T 1 ,
UP 1 = Internal energy of products at temperature T 1 ,
UR 2 = Internal energy of reactants at temperature T 2 ,
UP 2 = Internal energy of products at temperature T 2 ,
∆U 0 = Constant volume heat of combustion,
Q = Heat transferred to the surroundings during the process, and
W = Work obtained during combustion process.
Analysis for a non-flow process involving combustion at ‘constant volume’ :
When the combustion process is carried out at constant volume then the non-flow energy
equation, Q = (U 2 – U 1 ) + W, can be applied to give
Q = (UUPR 00 − ) ...(11.12)
where, W = 0 for constant volume combustion,
U 1 = UR 0 , and
U 2 = UP 0.
The internal energy change is independent of the path between the two states and depends
only on the initial and final values and is given by the quantity Q. This is illustrated in Fig. 11.2
and property diagram of Fig. 11.3. The heat so transferred is called the internal energy of combus-
tion at T 0 (or constant volume heat of combustion), and is denoted by ∆U 0. Thus,
∆U 0 = UP 0 – UR 0 ...(11.13)