Modern Engineering Thermodynamics

5.9 The Explosive Energy of Pressure Vessels 159
Exercises
10. Determine the final temperature of the helium in Example 5.7 when the sphere is left in the cold water for 10.0 s rather
than 5.00 s. Answer: T 2 = 16:6°C.
11. Determine the final temperature in the sphere in Example 5.7 after 5.00 s of immersion in the cold water if the sphere is
filled with air instead of helium (everything else remains the same). Answer: T 2 = 60°C.
12. Describe in words how the solution to Example 5.7 changes if the material in the sphere is an incompressible liquid
instead of an ideal gas. Answer: Change c v to c and the rest of the solution is the same.
5.9 THE EXPLOSIVE ENERGY OF PRESSURE VESSELS
The explosion of a pressure vessel, suchasasteamboiler,isanexampleofaveryunsteadystateprocess.But,
since it is such an important topic from a safety point of view, it is treated as a separate subject here.
Not many engineers realize just how dangerous a high-pressure gas or vapor can be. The explosive energy of a
pressure vessel is defined to be its capacity to do work adiabatically on its surroundings. Consider a pressure vessel
whose initial state is just before the explosion and whose final state is immediately after all the debris has
come to rest and thermodynamic equilibrium has been reestablished. The explosion process is considered to be
adiabatic with no net change in system kinetic or potential energies. The explosive energy can be determined
from the closed system energy balance as
Explosive energy = − 1 W 2 = mðu 1 − u 2 Þ
where we have introduced the minus sign because we want the work done by the system on the environment not
that done on the system. The explosive energy per initial unit volume of the pressure vessel is defined to be Γ, where
Γ = mðu 1 − u 2 Þ/V 1
= ðu 1 − u 2 Þ/v 1 (5.1)
If the pressure vessel contains an ideal gas with constant specific heats, then Eqs. (3.38) and (3.35b) can be used
to give the explosive energy per unit volume as
ðΓÞ ideal gas = c v ðT 1 − T 2 Þ/ðRT 1 /p 1 Þ = p 1 ð1 − T 2 /T 1 Þ/ðk − 1Þ (5.2)
where R/c v = k – 1. If, on the other hand, the pressure vessel contains an incompressible liquid, then Eq. (3.33)
can be used to give
ðΓÞ incompressible liquid = cðT 1 − T 2 Þ/v = ρcðT 1 − T 2 Þ (5.3)
A liquid that does not change phase during decompression undergoes the process very nearly isothermally, so
T 2 = T 1 and its explosive energy is zero. Therefore, the explosive energy of high-pressure liquids is very slight in
comparison with gases and vapors at the same pressure, and this is why liquids are often used to hydrostatically
test pressure vessels to failure.
EXAMPLE 5.8
On March 10, 1905, a catastrophic boiler explosion occurred
in a shoe factory in Brockton, Massachusetts, that killed 58
andinjured150people(Figure5.8). 2 This and similar
explosions brought about the development of the ASME
Boiler and Pressure Vessel Code in 1915. Suppose that the
Brockton shoe factory had a 250. ft 3 boiler and right before
the explosion it contained superheated steam at 600. psia
and 800.ºF. After the explosion, the steam quickly condensed
into saturated liquid water at 70.0ºF.
a. Determine the explosive energy per unit volume of
superheated steam.
b. How many 1 lbm sticks of TNT would it take to equal the
explosion of the boiler? The explosive energy per unit
mass of TNT is 1400. Btu/lbm.
Solution
First, draw a sketch of the system.
FIGURE 5.8
Example 5.8, Brockton Shoe Factory.
(Continued )