# What is the volume of the gas after the explosion in the following problem?

## In a thermonuclear device the pressure of 0.050 liters of gas within the bomb casing reaches $4.0 x {10}^{6}$ atm. When the bomb casing is destroyed by the explosion. the gas is released into the atmosphere where it reaches a pressure of 1.00 atm.

Nov 5, 2016

The volume of the gas is ${\text{200 m}}^{3}$.

#### Explanation:

This appears to be a Boyle's Law problem.

Boyle's Law is

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} {P}_{1} {V}_{1} = {P}_{2} {V}_{2} \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

We can rearrange Boyle's Law to get

V_2 = V_1 × P_1/P_2

In this problem,

P_1 = 4.0 × 10^6color(white)(l) "atm"; V_1 = "0.050 L"
${P}_{2} = \text{1.00 atm"; color(white)(mmll) V_2 = "?}$

${V}_{2} = {\text{0.050 L" × (4.00 ×10^6 color(red)(cancel(color(black)("atm"))))/(1.00 color(red)(cancel(color(black)("atm")))) = "200 000 L" = "200 m}}^{3}$