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ME444-Assignment #2-Sol September 16, 2014 1. Your classroom has dimensions of 3m x 8m x 12m. On a given day the relative humidity is 70%, pressure is 0.1 MPa and the temperature is 30C. Calculate the humidity ratio, the dew point, the mass of air and the mass of the water vapor. If the water vapor were condensed into liquid, how many liters of liquid would one expect? Solution The volume of the room is: 3𝑚 × 8𝑚 × 12𝑚 = 288 𝑚2 𝑝𝑣 𝑃𝑔 → 𝑝𝑣 = 0.7(4.246) = 2.972 𝑘𝑃𝑎 ∅= Dew point is the sat. temperature at =𝑃𝑣 = 2.972 𝑘𝑃𝑎. We can get the temperature by interpolation as: 2.972 − 2.339 𝑇 − 20 = 3.169 − 2.339 25 − 20 𝑇 = 23.81 °𝐶 Also partial pressure of air can be calculated from 𝑃 = 𝑃𝑣 + 𝑃𝑎 . 𝑃𝑎 = 100 − 2.972 = 97.028 𝑘𝑃𝑎 Humidity ratio is: 𝑃𝑣 𝑤 = 0.622 𝑃𝑎 2.972 𝑤 = 0.622 = 0.0191 97.028 Therefore mass of air can be calculated as below: 𝑃𝑎 𝑉 97.028 (288) = = 321 𝑘𝑔 𝑅𝑎 𝑇 0.287(303) 𝑚𝑣 = 𝑤 𝑚𝑎 = 0.0191(321 𝑘𝑔) = 6.13 𝑘𝑔 𝑚𝑎 = 1 ME444-Assignment #2-Sol September 16, 2014 𝑉𝑣 = 𝑚𝑣 𝑣𝑓 @𝑝𝑣 𝑣𝑓 − 0.001002 2.972 − 2.339 = 3.169 − 2.339 0.001003 − 0.001002 𝑣𝑓 = 0.0010027 𝑘𝑔 𝑉𝑣 = 6.146𝐸 − 3 3 = 6.146 𝐿 𝑚 2. Calculate the theoretical air–fuel ratio for the combustion of octane, C8H18. Solution The combustion equation is C8H18 + 12.5O2 + 12.5(3.76) N2 → 8 CO2 + 9H2O + 47.0N2 The air–fuel ratio on a mole basis is AF = (12.5 + 47.0)/1= 59.5 kmol air/kmol fuel The theoretical air–fuel ratio on a mass basis is found by introducing the molecular mass of the air and fuel. AF = 59.5(28.97)/114.2= 15.0 kg air/kg fuel 3. Determine the molal analysis of the products of combustion when octane, C8H18, is burned with 200% theoretical air, and determine the dew point of the products if the pressure is 0.1 MPa. Solution The equation for the combustion of octane with 200% theoretical air is C8H18 + 12.5(2) O2 + 12.5(2)(3.76) N2 → 8 CO2 + 9H2O + 12.5O2 + 94.0N2 Total kmols of product = 8 + 9 + 12.5 + 94.0 = 123.5 Molal analysis of products: CO2 = 8/123.5 = 6.47% H2O = 9/123.5 = 7.29% O2 = 12.5/123.5 = 10.12% N2 = 94/123.5 = 76.12% 100.00% 2 ME444-Assignment #2-Sol September 16, 2014 The partial pressure of the water is 100(0.0729) = 7.29 kPa, so the saturation temperature corresponding to this pressure is 39.7 °𝐶, which is also the dew-point temperature. 3