Page 354 - Advanced Thermodynamics for Engineers, Second Edition

344 CHAPTER 15 COMBUSTION AND FLAMES

15.6 PROBLEMS

P15.1 (a) What is meant by the terms
(i) a global reaction;
(ii) an elementary reaction;
(iii) a reaction mechanism.
(b) Describe the steps required to form a chain reaction and explain why chain reactions are
important in combustion.
(c) A reaction is found to be 25 times faster at 400 K than at 300 K. Measurements of the
temperature exponent yielded a value of 0.7. Calculate the activation energy of the
reaction. How much faster will the reaction be at 1000 K?
P15.2 A combustible mixture of gas and air is contained in a well-insulated combustion bomb. It is
ignited at a point and a thin flame propagates through the mixture completely burning the
reactants. This mechanism produces multiple zones of products: prove that the temperature of
an element of gas mixture which burned at pressure, p b , has a temperature, T(p, p b )ata
pressure, p > p b

k 1 k 1
" #
k Q 0 k
p b p
p
T p; p b ¼ T 1 þ
p 1 c p p b
where
k ¼ ratio of specific heats,
Q ¼ calorific value of fuel,
0
p
and suffix 1 defines the conditions before ignition.
Calculate the final pressure, p 2 , in terms of p 1 , T 1 , Q , c v and k. What is the difference
0
p
between the final temperature and that of the first gas to burn if T 1 ¼ 300 K, k ¼ 1.3 and
Q =cv ¼ 1500 K.
0
p
P15.3 The structure of ethylene is H 2 C ¼ CH 2 . Estimate the enthalpy of reaction when 1 kmol of
ethylene is completely oxidised. Compare the value obtained with the tabulated value of
1323.2 MJ/kmol. Give reasons for the difference between the values.
Neglecting dissociation, find the temperature reached after constant pressure combustion of
ethylene with 50% excess air if the initial temperature of the reactants is 400 K. The specific
heat at constant pressure of ethylene is approximately 1.71 kJ/kg K over the temperature
range of the reactants.
[1302.3 MJ/kmol; 2028 K]
P15.4 Describe the construction of a boiler for burning pulverised coal. Explain how this design
optimises the temperature, turbulence and time required for good combustion. What are the
main emissions from this type of plant, and how can they be reduced.