A fuel gas containing 75.0 mole% methane and the balance ethane is burned comple
ID: 702746 • Letter: A
Question
A fuel gas containing 75.0 mole% methane and the balance ethane is burned completely with 35.0% excess air.
The stack gas leaves the furnace at 800.0°C and is cooled to 350.0°C in a waste-heat boiler, a heat exchanger in which heat lost by cooling gases is used to produce steam from liquid water for heating, power generation, or process applications.
Take as a basis 100.0 mol of the fuel gas fed to the furnace.
The amounts of each of the following gases leaving the furnace at 800.0°C:
Taking as a basis of calculation 100.0 mol of the fuel gas fed to the furnace, calculate the amount (magnitude) of heat (MJ) that must be transferred from the gas in the waste heat boiler to accomplish the indicated cooling. ? MJ
O2 83.1 mol N2 1205 mol CO2 125 mol H2O 225 molExplanation / Answer
We calculate the mole fractions of each component:
Total moles = 83.1 + 1205 + 125 + 225 = 1638.1 mol
xO2 = 83.1/1638.1 = 0.050703
Similarly,
xN2 = 0.7356
xCO2 = 0.076308
xH2O = 0.1374
From internet, we find specific heat values:
Cp,O2 = 34.08 J/mol-K
Cp,N2 = 37.49 J/mol-K
Cp,CO2 = 52.228 J/mol-K
Cp,H2O = 39.276 J/mol-K
Taking 1 mole of gas as basis, since mole fractions are calculated by this, Heat transfer
Q = (xO2*Cp,O2 + xN2 *Cp,N2 + xCO2 *Cp,CO2 + xH2O *Cp,H2O)*(800 - 350)
= 38.6875 * (800-350)
= 17409.39 J --- for 1 mole
For 100 mol,
Q = 17409 * 100 = 1740900 J
= 1.7409 MJ --- Ans