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Q. 3

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 566

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Short Answer

At what pressure will the mean free path in room-temperature nitrogen be ?

At the pressure of the mean free path in room-temperature nitrogen be

See the step by step solution

Step by Step Solution

Step 1: Given Information 

Nitrogen room temperature

Mean free path

Step 2: Explanation

Molecular density determines how tightly the atoms are bonded in a system. It is determined by equation (18.2) in the form of the number of atoms per cubic meter in a system.

According to the ideal gas law, the volume of the container , the pressure exerted by the gas, the temperature of the gas, and the number of moles of the gas in the container are all related.

is Boltzmann's constant and in SI unit its value is

Due to collisions with other molecules, a molecule undergoing distance travel experiences a delay between diffusing to a different position due to these collisions.

The molecules need a certain amount of time to diffuse to a new position.

In equation (20.3), the mean free path is the distance the molecules travel between collisions on average.

Radius of the molecule,

Number of molecules


Diatomic gas of nitrogen's radius is,

If , then the answer to equation (3) is , which gives us the equation for the pressure

Step 2: Explanation

To convert Celsius to Kelvin, we must first convert the units between the two scales. Kelvins are the units for the Kelvin scale. It can be converted between the two scales by using equation (18.7).

Substitute the value for into equation (5) to get

Put the values for and into equation (4) to get

Step 4: Final Answer

Hence, if the mean free path in room temperature of nitrogen then the pressure is.

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