A volume analysis of the exhaust gases from an internal combustion engine gave t

Question

A volume analysis of the exhaust gases from an internal combustion engine gave the following proportions: 11% carbon dioxide (CO_2), 7% carbon monoxide (CO), 2% oxygen (O_2), and 80 % nitrogen (N_2). The volume, mass and temperature of the mixture of gases are 5 m^3, 10 kg and 800 K, respectively. Using the steam tables and showing all your calculations: i) Copy and complete Table B.1 in order to determine the mass fraction m_i/m of each constituent gas. Assume that the amount of substance for the mixture of gases, n, is 1 kmol. ii) Calculate the mean specific heat capacity at constant pressure, C_p, the specific gas constant, R, and the specific heat capacity at constant volume, C_v, for the mixture of exhaust gases. iii) Determine the pressure of the mixture of exhaust gases.

Explanation / Answer

by considering 1 mole of gas as the basis and noting that volume% = mole %, the following calculations are done

Average specific heats CP ( specific heat at cosntant pressure ) ( in Kj/Kg.K) : CO2=0.844, CO =1.02, N2=1.04, O2=0.919

Average specific heat= sum of mass frction of gas* specific heat of that gas

=0.844*0.11+0.07*1.02+0.02*1.04+0.8*0.919=0.92

Average specific heat CV( specific heat at constant volume) ( in Kj/Kg.K): CO2=0.655, CO=0.72,

N2= .743, O2=0.659

Average specific hear= 0.11*0.655+0.07*0.72+0.02*0.743+0.8*0.659=0.6853

Average gas constant, CP-CV= R = 0.92-.6853=0.23494 KJ/kg.K

Specific gas constant,R ( KJ/kg.K): CO2= 0.844-0.655= 0.189, CO= 1.02-0.72=0.3, 1.04-0.743= .31, O2= 0.919-0.659=0.26

From gas law, PV= nRT

V= 5m3= 5000 L, n= mass/molar mass ( from the tables of mass, moles= mass/ molar mass, for 1 mole, mass/molar mass=1, mass = molar mass= 29.84, moles= 10*1000 gm/ 29.84 gmole = 335 gmoles, R= 0.0821 L.atm/mole.K, T= 800K, P= nRT/V= 335*0.0821*800/5000 atm=4.4 atm

Gas Volume % Volume fraction Molar mass moles Mass= moles* molar mass substnace per kmole Mass fraction CO2 11 0.11 44 0.11 4.84 4.84 0.162198391 CO 7 0.07 28 0.07 1.96 1.96 0.065683646 O2 2 0.02 32 0.02 0.64 0.64 0.021447721 N2 80 0.8 28 0.8 22.4 22.4 0.750670241 sum 100 1 29.84 1

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