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In a period of 6.00 s, 9⋅1023 nitrogen molecules strike a section of a wall with an area o...

In a period of 6.00 s, 9⋅1023 nitrogen molecules strike a section of a wall with an area of 2.00 cm2. If the mol ecules move with a speed of 400.0 m/s and strike the wall head on in elastic collisions, what is the pressure exerted on the wall? (The mass of one N2 molecule is 4.68 ⋅ 10−26 kg.)

Step-by-Step Solution

Solution 1
Step #1 of 6

THINK

Given in a period of, there are nitrogen molecules strike a section of a wall with an area of. The molecules move with a speed of and strike the wall head on in elastic collisions, and then the pressure exerted on the wall can be calculated by the law of conservation of linear momentum and Newton’s second law of motion.

Step #2 of 6

RESEARCH

If is the average force acting on the wall of area, then the average pressure exerted on the wall is given by

…… (1)

According to Newton’s second law of motion, the force is defined as the rate of change of momentum and is given by

…… (2)

Here is the change in momentum in a time interval of.

Step #3 of 6

If is the initial velocity of molecule and be the final velocity of the molecule of mass, then the change in momentum is

…… (3)

Here the molecules move so rapid, that even after collision their speed remains same but direction is reversed, that is

Hence the change in momentum is given by

Hence the average force per single molecule is given by

…… (4)

Step #4 of 6

If there are number of molecules in total, then the average force is given by

…… (5)

Hence the average pressure exerted on the wall is

…… (6)

Step #5 of 6

CALCULATE

Time period

Number of molecules,

Area of the wall,

The speed of the molecule,

The mass of one nitrogen molecule,

Step #6 of 6

Substituting all the known values in the equation (6), the average pressure exerted on the wall is given by

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