A spherical steel bomb with inside diameter equal to $20\;$ cm is full of nitroglycerin ($\rho = 1.6\frac{g}{cm}^3)$. Assuming that the temperature at the time of the break is worth $2000^oC$, calculate the pressure developed at that time assuming the ideal gas law is applicable (which is not the case in these conditions!)
Calculate first the volume of the bomb !
$V$ $=$ $\frac{4\pi r^3}{3}$ $=$ $\frac{4\cdot 3.14\cdot 10^3}{3}$ $=$ $4187\;cm^3$
Calculate the mass and the number of moles of nitroglycerin !
$m$ $=$ $4187\cdot 1.6\; g$ $n$ $=$ $\frac{4187\cdot 1.6}{227}$ $=$ $29.5\; mol$
Calculate the pressure (in bar) at the time of the break !
$P$ $=$ $\frac{nRT}{V}$ $=$ $\frac{29.5\cdot 8.3 \cdot 2273.15 }{0.004187}$ $=$ $132900000 \frac{N}{m^2}$ $=$ $13290 \;bar$