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Thus, the higher heating value for the specified fuel gas is 285.6 Btu/ft3. (c) The density of any ideal gas can be calculated by modifying the ideal gas law, presented below: PV = nRT Because density is simply the mass of a substance divided by its volume, multiply both sides of the ideal gas equation by the molecular weight, MW, of the gas mixture. Recall that the moles of a substance, n, times its molecular weight equals its mass. PV(MW) = n(MW)RT PV(MW) = (mass)RT Rearrange this equation to derive an ideal gas law equation that will calculate the density of any ideal gas given the temperature, pressure and MW: density = mass = P(MW) volume RT The selection of the ideal gas constant, R, in convenient units such as (atm-ft3)/(lb mol-R) will simplify the density calculation in units of lbs per ft3 P(MW) RT (1 atm)(10.56 lb ) lbmol lb = 0.02781 3 (at 1 atm, 60 o F) = (d) The HHV in Btu/lb can be calculated from the HHV in Btu/ft3 and the density: ⎛ Btu⎞⎛ 1ft3 ⎞ Btu HHV = ⎜⎝ 285.6 ft 3 ⎟⎠⎜ 0.02781 lb ⎟ = 10,270 lb (e) The LHV can be calculated by recalling that the fundamental difference between HHV and LHV is the state of the product water. That is, HHV is based on a liquid water product, while LHV is based on a gaseous water product. Because energy is consumed to evaporate liquid water into gaseous water, LHV values are always less than or equal to HHV values. To convert liquid water to water vapor at 1 atm and 60 oF requires approximately 1050 Btu/lb, or 50 Btu/ft3 of water vapor. For a given gas mixture, the quantitative difference between the HHV and LHV is, obviously, a function of how much water is produced by the given fuel. So the first step in converting HHV to LHV is the determination of the amount of water produced by the fuel. This is done in the table below. The LHV to HHV adjustment is calculated by multiplying the water volume times the change in enthalpy going from liquid to vapor (50 Btu/ft3): density = (0.7302 atm-ft3 )(60 + 460 R) lbmol-R ft ⎝⎠ 9-24PDF Image | Fuel Cell Handbook (Seventh Edition)
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