Question

A typical family car has four cylinders with a total cylinder volume of 1600 cm³ and a fuel consumption of 7.0 l per 100 km when driving at a speed of 90 km/h. During one second each cylinder goes through 25 burn cycles and consumes 0.4 g of fuel. Assume that fuel consists of 2,2,4-trimethylpentane,C₈H₁₈.The compression ratio of the cylinder is 1:8. 

(a) Calculate the air intake of the engine (m³/s). The gasified fuel and air are introduced into the cylinder when its volume is largest until the pressure is 101.0 kPa. Temperature of both incoming air and fuel are 100°C. Air contains 21.0 % (by volume) of O₂ and 79.0 % of N₂.It is assumed that 10.0 % of the carbon forms CO upon combustion and that nitrogen remains inert. 

(b) The gasified fuel and the air are compressed until the volume in the cylinder is at its smallest and then ignited. Calculate the composition (% by volume) and the temperature of the exhaust gases immediately after the combustion (exhaust gases have not yet started to expand). The following data is given: 

Compound	∆Hf (kJ/mol)	Cp (J/mol K)
O2(g)	0.0	29.36
N2(g)	0.0	29.13
CO(g)	-110.53	29.14
CO2(g)	-395.51	37.11
H2O(g)	241.82	33.58
2,2,4-trimethylpentane	-187.82

(c) Calculate the final temperature of the leaving gases assuming that the piston has moved to expand the gases to the maximum volume of the cylinder and that the final gas pressure in the cylinder is 200 kPa. 

(d) To convert CO(g) into CO₂(g) the exhaust gases are led through a bed of catalysts with the following work function:  

n(CO)/nCO₂) = 1/4 k [n(CO)/n(CO₂]₁ Ve ^-t/to

where [n(CO) / n(CO₂)]₁ is the molar ratio before the catalyst, v is the flow rate in mol/s and T the temperature of the gases entering the catalyst (the same as the temperature of the leaving exhaust gases). T₀ is a reference temperature (373 K) and k is equal to 3.141 s/mol. Calculate the composition (% by volume) of the exhaust gases leaving the catalyst.

Answer 1

(a) M_r(C₈H₁₈) = 114.0, 

 Cylinder volume (V₀) = 4.00 × 10^-4 m³, p₀ = 101 000 Nm^-2, T₀ = 373 K 

Considering one cylinder during one burn cycle one obtains (f = fuel): 

m_f = 0.400/25 g = 0.0160g, n_f = 1.4004 × 10^-4 mol 

(m_f = mass of fuel, n_f = amount of substance of fuel) 

nG = nf + nA = p0V0 / (RT0) = 0.0130 mol 

(n_G = number of moles of gases, n_A = moles of air) 

⇒ n_A = 0.0129 mol 

⇒ Air intake of one cylinder during 25 burn cycles: 

VA = 25 n_A R T₀ / p₀ = 9.902 ×10^-3 m³ /s

 ⇒ The air intake of the whole engine is therefore: V_total = 4 VA = 0.0396 m³/s 

(b) The composition of the exhaust gases of one cylinder during one burn cycle is considered: 

before:

Amounts of substances (in mol) before and after combustion: 

	C8H18	O2	CO	CO2	H2O
before	1.404 ×10-4	2.709 × 10-3	0	0	0
after	0	10.10 × 10-4	1.123 × 10-4	10.11 × 10-4	12.63 × 10-4

The composition of the gas after combustion is therefore: 

Componen t	N2	O2	CO	CO2	H2O	Total
mol × 104	101.91	10.10	1.12	10.11	12.63	135.87
%	75.0	7.4	0.8	7.5	9.3	100

From thermodynamics the relation between the enthalpy and temperature change is given by 

(c) The final temperature of the leaving gases from one cylinder: 

p₂ = 200 000 Pa, V₀ = 4.00 × 10^-4 m³ ,  

n_G = moles of exhaust gases in one cylinder = 0.01359 mol 

(d) The flow from all four cylinders is given: v = 4 × 25 × n_G = 1.359 mol/s, so that 

0.01772 (40.44 + x) = 4.48 + x ⇒ x = 3.70 

Thus, the composition of the gas after the catalyst is: