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.

1 Answer
Nov 5, 2016

Answer:

The volume of the gas is #"200 m"^3#.

Explanation:

This appears to be a Boyle's Law problem.

Boyle's Law is

#color(blue)(bar(ul(|color(white)(a/a)P_1V_1 = P_2V_2color(white)(a/a)|)))" "#

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 ="1.00 atm"; color(white)(mmll) V_2 = "?"#

#V_2 = "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#