Energy Released on the Explosion of a Compressed Air Tank

A compressed air tank has a volume of 0.167 $m ^{3}$ and contains air at 25°C and 650 bar when it explodes. Estimate the amount of work done on the surroundings in the explosion. Compute the TNT equivalent of the compressed air tank blast.

Data: For air $C_{ P }^{*}=29.3 J /( mol K ) \text { and } \gamma=C_{ P }^{*} / C_{ V }^{*}=1.396$ .

Question

Energy Released on the Explosion of a Compressed Air Tank

A compressed air tank has a volume of 0.167 [latex]m ^{3}[/latex] and contains air at 25°C and 650 bar when it explodes. Estimate the amount of work done on the surroundings in the explosion. Compute the TNT equivalent of the compressed air tank blast.

Data: For air [latex]C_{ P }^{*}=29.3 J /( mol K ) ext { and } \gamma=C_{ P }^{*} / C_{ V }^{*}=1.396[/latex].

Accepted Answer

[latex]\begin{aligned}-W &=\frac{650 bar imes 0.167 m ^{3}}{(1.396-1)}\left[1-\left(\frac{1 bar }{650 bar } ight)^{(1.396-1) / 1.396} ight] \&=230.2 bar m ^{3} imes 10^{5} \frac{ Pa }{ bar } imes \frac{1 \frac{ J }{ m ^{3}}}{ Pa } imes \frac{1 kJ }{10^{3} J }=23020 kJ\end{aligned}[/latex]

Therefore, the blast energy is equivalent to

[latex]\frac{23020 kJ }{4600 \frac{ kJ }{ kg TNT }}=5.0 kg ext { of TNT }[/latex]

Clearly, this is a sizable explosion. In fact, a blast of 5 kg of TNT will cause the total destruction of structures not reinforced to withstand blasts within a circle of radius 7 meters from the blast site, substantial damage out to a radius of 14 meters, minor structural damage out to 55 meters, and broken windows out to 130 meters. Also, eardrum ruptures can be expected up to 10 meters from the site of the explosion.

Question 5.4.2: Energy Released on the Explosion of a Compressed Air Tank A ...

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