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Question

A beam of hydrogen molecules is directed toward a wall, at an angle 32 with the normal to the wall. Each molecule in the beam has a speed of 1.0 km/s and a mass of 3.3×1024g. The beam strikes the wall over an area of 2.0 Cm2, at a rate of 4.0×1023 molecules per second. What is the beam's pressure on the wall?


A

11 kPa

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B

1 kPa

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C

9 kPa

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D

13 kPa

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Solution

The correct option is A

11 kPa


We need the pressure on that 2 cm2 patch on the wall. But by definitions,

Pressure P=[forcearea]per molecule×number of molecules.

=[rate of change of momentumarea]per molecules×N

[mvfinalmvinitialarea×time]per molecules×N

=[2×(3.3×1027 kg)×1000 m/s×cos32(2×104m2)×1s]×(4×1023)Pa

=11.2×103 Pa11 kPa.


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