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82.575 - Fire Dynamics I // Problem Set 1
Distributed:
Thursday January 17, 2002
Due:
Thursday February 07, 2002
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1.
An arsonist pours 1 litre of heptane C7H16 (gasoline) in a small pan in a room with floor
dimensions of 4.0 m x 6.0 m and height 3.0 m. Assume the room is airtight, so that gas
cannot enter or leave the room. Determine whether there is enough O2 in the room for
the complete combustion of the heptane?
2. Suppose 1 kg of polyvinyl chloride (PVC) is burned in a room with floor dimensions of
4.0 m x 6.0 m and height 3.0 m. Calculate the number of moles of HCl and the number of
moles of CO generated. Assume the room is airtight and the smoke is mixed uniformly
throughout the room. Use the toxicity models presented in class to determine which of the
2 gases (HCl or CO) would pose the greater threat to life.
Hint: Following combustion the mass of gas in the room will equal the sum of the mass of PVC
and the mass of air in the room before combustion. Assuming the molecular weight of the fire gas
is still 28.95 g/mol, the total number of moles in the room following combustion can be computed.
3.
Suppose 1 kg of polystyrene (PS) is burned the same room as in Question 1. Calculate
the heat released, and the mass of CO and soot generated. Calculate the time occupants
could remain in the room without being incapacitated by CO. Calculate the visibility in
the room. Calculate the temperature of the gas in the room assuming an adiabatic process
(no heat loss to the walls, ceiling or floor). The specific heat of the fire can be assumed
to be that of air, namely 1.0 kJ kg-1 K-1.
4.
Calculate the boiling point of liquid heptane (n-C7H16). [As there are no data for heptane
in the Table on page 2-17 of the class notes, you will have to use engineering judgement
to estimate E and F.]
5.
Derive the chemical equation for the complete combustion of the general alkane CnH2n+2.
From this equation, derive general expressions for the yield of CO2, the yield of H2O and
the consumption of O2 for the complete combustion of CnH2n+2. Using this expression,
compute the yield of CO2, the yield of H2O and the consumption of O2 for the first 5
alkanes (n = 1 to 5) and for very large n (that is, as n  ). Summarise your findings in
tabular form as follows:
n
1
2
3
4
5

CnH2n+2
CH4
C2H6
C3H8
C4H10
C5H12
CnH2n+2
Yield of CO2 (g/g)
Yield of H2O (g/g)
Consumption of O2 (g/g)
From your predictions for the consumption of O2 as n  , compute the net heat of
combustion (per g of PE burned) for the complete combustion of polyethylene.