# 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.)

## Answers and Replies

This question can just as easily be solved by considering it kinematically as it can through a kinetic theory of gases perspective. Anyways, basically the jist of it is that, for each bullet, superman has to change its momentum by 2mv (mv to stop is and another mv to get it going back in the opposite direction at the same speed). Over the course of a minute he does this 150 times. so the total force divided by the total time

This question can just as easily be solved by considering it kinematically as it can through a kinetic theory of gases perspective. Anyways, basically the jist of it is that, for each bullet, superman has to change its momentum by 2mv (mv to stop is and another mv to get it going back in the opposite direction at the same speed). Over the course of a minute he does this 150 times. so the total force divided by the total time

Well, I thought about solving it this way, but my professor wants me to relate these problems to thermal physics :(

Any help?