W ¼
Z V f
V i
p 0 dV ¼ p 0 V f À V i
À
Á
¼ p 0 V i
V f
V i
À 1
,
ð5:65Þ
where V i and V i are the initial and final volumes, respectively. Assuming the
expansion is adiabatic we have
V f
V i
¼
p
p 0
1=γ
,
ð5:66Þ
hence, the work done by unit volume of the compressed air is
Fig. 5.8 A plot showing the fraction of the energy wasted when the shock front has expanded to a
radius where the blast pressure (in atmospheres) is y 1 (γ ¼ 1.4)
5.14 The Wasted Energy
247
Z V f
V i
p 0 dV ¼ p 0 V f À V i
À
Á
¼ p 0 V i
V f
V i
À 1
,
ð5:65Þ
where V i and V i are the initial and final volumes, respectively. Assuming the
expansion is adiabatic we have
V f
V i
¼
p
p 0
1=γ
,
ð5:66Þ
hence, the work done by unit volume of the compressed air is
Fig. 5.8 A plot showing the fraction of the energy wasted when the shock front has expanded to a
radius where the blast pressure (in atmospheres) is y 1 (γ ¼ 1.4)
5.14 The Wasted Energy
247