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Thermodynamic properties are essential characteristics that define the state and behavior of substances and systems within the realm of thermodynamics. These properties include pressure, temperature, volume, internal energy, and enthalpy, among others. For fuel mixtures, specific properties such as lower heating value are crucial for understanding energy output during combustion. Lower Heating Value (LHV) represents the amount of usable energy obtained from a fuel excluding the energy from condensing the water vapor in the fuel. It is an important factor in calculating the efficiency and performance of fuel-powered systems.

A fuel mixture is a combination of different hydrocarbon molecules that make up the fuel. The composition of a fuel mixture is expressed in terms of molar fractions. These fractions indicate the proportion of each component present. In our example, the fuel mixture consists of 85% methane (CH4), 10% ethane (C2H6), 2% propane (C3H8), and 3% nitrogen (N2). It's important to note that nitrogen does not contribute to the heating value because it is inert and not a fuel. Understanding the composition allows us to calculate the overall energy content and other thermodynamic properties of the mixture.

Molar fraction represents the ratio of moles of a particular component to the total moles in a mixture. It's a way to express the composition of each substance within the mixture. Mathematically, the molar fraction is given by: \[\text{Molar Fraction (X_i)} = \frac{n_i}{n_{total}}\] where \(n_i\) is the moles of component \(i\) and \(n_{total}\) is the total moles of the mixture. For our exercise: \ \ -Ch4: 0.85 \ -C2H6: 0.10 \ -C3H8: 0.02 \ -N2: 0.03 Molar fractions are key to calculating average properties such as molecular weight and heating value of the mixture. By multiplying the LHV of each component by its molar fraction, we can find its contribution to the total LHV.

The molecular weight of a mixture is the weighted average of the molecular weights of its components, based on their respective molar fractions. This can be determined using the following equation: \[\text{MW_{mixture}} = \text{Σ (Molar Fraction } \times \text{Molar Mass)}\] For our mixture: \ -CH4: (0.85 \times 16) \ -C2H6: (0.10 \times 30) \ -C3H8: (0.02 \times 44) \ -N2: (0.03 \times 28) Summing up these contributions, we get the total molecular weight of 17.36 g/mol. This average molecular weight is pivotal for converting energy values from a molar basis to a mass basis, enabling calculations in practical units like kJ/kg.