Question

A mixture of 40 percent by volume methane \(\left(\mathrm{CH}_{4}\right),\) and 60 percent by volume propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right),\) is burned completely with theoretical air and leaves the combustion chamber at \(100^{\circ} \mathrm{C}\). The products have a pressure of \(100 \mathrm{kPa}\) and are cooled at constant pressure to \(39^{\circ} \mathrm{C} .\) Sketch the \(T\) -s diagram for the water vapor that does not condense, if any. How much of the water formed during the combustion process will be condensed, in kmol \(\mathrm{H}_{2} \mathrm{O} / \mathrm{kmol}\) fuel?

Short answer

Answer: 3.2 kmol H₂O/kmol fuel

Step-by-step solution

Determine the amount of water formed during combustion.

We first need to determine how much kmol of water is produced after the combustion of the given mixture of methane and propane using stoichiometric reactions. The balanced equations for the complete combustion of methane and propane are as follows: \(CH_{4} + 2O_{2} + 7.52N_{2} \to CO_{2} + 2H_{2}O + 7.52N_{2}\) \(C_{3}H_{8} + 5O_{2} + 18.8N_{2} \to 3CO_{2} + 4H_{2}O + 18.8N_{2}\) 40% by volume of methane (CH4): 0.4 kmol 60% by volume of propane (C3H8): 0.6 kmol For methane: Number of kmol of water formed = 2 * 0.4 = 0.8 kmol H₂O For propane: Number of kmol of water formed = 4 * 0.6 = 2.4 kmol H₂O Total kmol of water formed during combustion = 0.8 + 2.4 = 3.2 kmol H₂O

Determine the state of steam at 39°C and 100 kPa and find out how much water condenses.

We use steam tables to find the properties of the steam at the given temperature and pressure. At 39°C (312.15 K) and 100 kPa: From the steam tables, the saturation temperature at 100 kPa is approximately 99.6°C, which is greater than the temperature of the steam (39°C). This indicates that steam is in the "compressed liquid" region, meaning that all of the water formed during the combustion process will be condensed. Therefore, the amount of water condensed during the combustion process is 3.2 kmol H₂O/kmol fuel. As all the water vapor is condensed, it is impossible to sketch a T-s diagram for the water vapor that does not condense, since there is no water vapor in the given conditions.