Question

The “Quick Fill” bicycle tire filling system consists of a small (2 cm diameter, 6.5 cm long) cylinder filled with nitrogen to a pressure of 140 bar. Estimate the explosion equivalent of the gas contained in the cylinder in grams of TNT. Assume nitrogen is an ideal gas.

Answer 1

Assuming that the explosion is isothermal in nature; the energy released is given by

E = P2V ln (P2 / P1)

Here;

P1 = ambient pressure = 1 bar

P2 = burst pressure = 140 bar

V = volume occupied by gas = πd2L / 4

V = π X 0.02 X 0.02 X 0.065 = 0.000082 m3

Substituting these values in the above equation;

E = 14000000 X 0.000082 ln (140/1)

E = 5673 J

We know that

1 gram of TNT releases 4184 J of energy

Therefore; the explosion equivalent of the gas contained in the cylinder in grams of TNT:

= 5673 / 4184

= 1.36 grams

Which is the required value