# Superman and the Kinetic Theory of Gases

## Homework Statement

Superman leaps in front of Lois Lane to save her from a volley of bullets. In a 1-minute interval, and automatic weapon fires 150 bullets, each of mass 8.0g, at 400 m/s. The bullets strike his mighty chest, which has an area of 0.75 m2. Find the average force exerted on Superman's chest if the bullets bounce back after an elastic, head-on collision.

## Homework Equations

Kinetic Theory of Gases: P = $$\frac{2}{3}$$($$\frac{N}{V}$$)(.5mv^2)

where .5mv^2 is the average kinetic energy per molecule.

## The Attempt at a Solution

After substituting values into the Kinetic Theory of Gases:

P = $$\frac{2}{3}$$($$\frac{N}{V}$$)(.5mv^2)

P = (2/3)(150 bullets/V)(.598.0g)(400m/s)^2

If V = 0.75m^2 * 1m = .75m^3, then P = 8.53 * 10^7 Pa.

However, the answer in the textbook is 16N, I'm just not sure if:
1. V (described above) is accurate.
2. There is an equation to relate work and pressure. (Note: This is a algebra-based course.)