Page 246 - Advanced thermodynamics for engineers

10.8 PROBLEMS 233

10.8 PROBLEMS

Assume that air consists of 79% N 2 and 21% O 2 by volume

P10.1 Calculate the lower heat of reaction at constant volume for benzene C 6 H 6 at 25 C. The

heats of formation at 25 C are: benzene, (C 6 H 6 ) 80.3 MJ/kmol; water vapour (H 2 O),

242 MJ/kmol; carbon dioxide (CO 2 ), 394.0 MJ/kmol.
A mixture of one part by volume of vaporised benzene to fifty parts by volume of air is
ignited in a cylinder and adiabatic combustion ensues at constant volume. If the initial
pressure and temperature of the mixture are 10 bar and 500 K respectively, calculate the
maximum pressure and temperature after combustion neglecting dissociation. (Assume the
internal energy of the fuel is 8201 kJ/kmol at 298 K and 12,998 kJ/kmol at 500 K)
[ 3170 MJ/kmol; 52.11 bar; 2580 K]
P10.2 The heat of reaction of methane (CH 4 ) is determined in a constant pressure calorimeter by
burning the gas as a very weak mixture. The gas flow rate is 70 L/h, and the mean gas

temperature (inlet to outlet) is 25 C. The temperature rise of the cooling water is 1.8 C,

with a water flow rate of 5 kg/min. Calculate the higher and lower heats of reaction at
constant volume and constant pressure in kJ/kmol if the gas pressure at inlet is 1 bar.
[ 800,049.5 kJ/kmol; 887,952 kJ/kmol]
P10.3 In an experiment to determine the calorific value of octane (C 8 H 18 ) with a bomb calorimeter
the mass of octane was 5.42195 10 4 kg, the water equivalent of the calorimeter
including water 2.677 kg and the corrected temperature rise in the water jacket 2.333 K.
Calculate the lower heat of reaction of octane, in kJ/kmol at 15 C.

If the initial pressure and temperature were 25 bar and 15 C, respectively and there was

400% excess oxygen, estimate the maximum pressure and temperature reached immediately
after ignition assuming no heat losses to the water jacket during this time. No air was present
in the calorimeter.
[ 5,099,000 kJ/kmol; 3135 K]
P10.4 A vessel contains a mixture of ethylene (C 2 H 4 ) and twice as much air as that required for
complete combustion. If the initial pressure and temperature are 5 bar and 440 K, calculate
the adiabatic temperature rise and maximum pressure when the mixture is ignited.
If the products of combustion are cooled until the water vapour is just about to
condense, calculate the final temperature, pressure and heat loss per kmol of original
mixture.
The enthalpy of combustion of ethylene at the absolute zero is 1,325,671 kJ/kmol; and
the internal energy at 440 K is 16,529 kJ/kmol.
[1631 K; 23.53 bar; 65 C; 3.84 bar; 47,119 kJ/kmol]

P10.5 A gas engine is operated on a stoichiometric mixture of methane (CH 4 ) and air. At the end of
the compression stroke the pressure and temperature are 10 bar and 500 K, respectively. If
the combustion process is an adiabatic one at constant volume, calculate the maximum
temperature and pressure reached.
[59.22 bar; 2960 K]