Modern Engineering Thermodynamics

160 CHAPTER 5: First Law Closed System Applications
EXAMPLE 5.8 (Continued )
The unknowns are explosive energy per unit volume of superheated steam and the number of 1 lbm sticks of TNT it would
it take to equal the explosion of the boiler. The system is closed, and the material is steam.
a. From the superheated steam table, Table C.3a of Thermodynamic Tables to accompany Modern Engineering Thermodynamics,
we find that at 600. psia and 800.ºF, u 1 = 1275:4 Btu/lbm and v 1 = 1:190 ft 3 /lbm; from the saturated steam table,
Table C.1a, we have u 2 = u f ð70°FÞ = 38:1 Btu/lbm. So Eq. (5.1) gives
Γ = ð1275:4 – 38:1Btu/lbmÞ/ð1:190ft 3 /lbmÞ = 1039:7 Btu/ft 3
b. For a 250. ft 3 boiler, the explosive energy is then ð1039:7 Btu/ft 3 Þð250: ft 3 Þ = 2:60 × 10 5 Btu. Therefore, it would take
ð2:60 × 10 5 BtuÞ/ð1400: Btu/lbmÞ = 186 one-pound sticks of TNT to match the boiler explosion.
Exercises
13. Using saturated liquid water at 70.0°F as the postexplosion state, determine the explosive energy per unit volume of
superheated steam at (a) 100. psia and 1000.°F, (b) 1000. psia and 1000.°F, (c) 80.0 MPa and 1000.°C. Answer:
(a) Γ = 154:0 Btu/ft 3 , (b) Γ = 1580 Btu/ft 3 , (c) Γ = 5:32 × 10 5 kJ/m 3 .
14. Determine the explosive energy of the boiler in Example 5.8 in lbm of TNT if it had a volume of 1500. ft 3 . Answer:
1114 lbm TNT.
15. How could Eq. (5.2) lead to an incorrect conclusion regarding the explosive energy (and danger) of a compressed ideal
gas? Answer: If the initial and final temperatures of the ideal gas before and after the explosion are taken to be the
same, then Γ = 0 and you would conclude that a compressed ideal gas is not dangerous. However, the final state of the
explosive process must be the state that occurs immediately after the debris from the explosion has come to rest. If we
model the explosion as a reversible and adiabatic process, we see in Chapter 7 that T 2 = T 1 ðp 2 /p 1 Þ ðk–1Þ/k , where k is the
specific heat ratio c p /c v , then Eq. (5.2) becomes
2
Γ ideal gas reversible & adiabatic = P 1 4
k − 1 1 − p 2
k−1
k
p 1
3
5
and the explosive danger of a compressed ideal gas becomes more apparent.
2 At about 8:00 AM there were around 400 employees at the R. B. Grover & Company shoe factory in Campello, when the boiler exploded, shot through the
roof, and caused the building to collapse. The boiler traveled several hundred feet, damaging a number of buildings and coming to rest in the wall of a
house. Thirty-six of the victims were never identified and were buried in a common grave, where a monument to the victims was later erected by the city.
SUMMARY
In this chapter, we investigate a series of closed system examples and carry out a first law analysis of them using
the energy balance or the energy rate balance. The primary purpose of these examples is to illustrate the material
presented in Chapter 4.
The only new equations introduced in this chapter are those associated with the explosive energy per unit initial
volume of pressure vessels, Γ, where in general
Γ = u 2 − u 1
v 1
(5.1)
and for ideal gases
or for incompressible liquids
Γ ideal gas = p
1
k − 1 1 − T
2
T 1
Γ incompressible liquid = cðT 1 − T 2 Þ
v
(5.2)
(5.3)