Question

A beam of hydrogen molecules is directed toward a wall, at an angle ${32}^{\circ }$ with the normal to the wall. Each molecule in the beam has a speed of 1.0 km/s and a mass of $3.3\times {10}^{24}g$. The beam strikes the wall over an area of $2.0C{m}^2$, at a rate of $4.0\times {10}^{23}$ molecules per second. What is the beam's pressure on the wall?

• A. 11 kPa
• B. 1 kPa
• C. 9 kPa
• D. 13 kPa

Answer 1

The correct option is A

11 kPa

We need the pressure on that $2c{m}^2$ patch on the wall. But by definitions,

$PressureP={\left[\frac{force}{area}\right]}_{permolecule}\times numberofmolecules.$

$={\left[\frac{rateofchangeofmomentum}{area}\right]}_{permolecules}\times N$

${\left[\frac{m{\overrightarrow{v}}_{final}-m{\overrightarrow{v}}_{initial}}{area\times time}\right]}_{permolecules}\times N$

$=\left[\frac{2\times (3.3\times {10}^{-27}kg)\times 1000m/s\times cos{32}^{\circ }}{(2\times {10}^{-4}{m}^2)\times 1s}\right]\times (4\times {10}^{23})Pa$

$=11.2\times {10}^{3}Pa\approx 11kPa.$