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Q. 41

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 568

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Short Answer

Photons of light scatter off molecules, and the distance you can see through a gas is proportional to the mean free path of photons through the gas. Photons are not gas molecules, so the mean free path of a photon is not given by Equation, but its dependence on the number density of the gas and on the molecular radius is the same. Suppose you are in a smoggy city and can barely see buildingsaway.

a. How far would you be able to see if all the molecules around you suddenly doubled in volume

b. How far would you be able to see if the temperature suddenly rose from to a blazing hot with the pressure unchanged?

a.The distance for the molecules around you suddenly doubled in volume is.

b.The distance for the temperature suddenly rose fromto a blazing hotwith the pressure unchanged is.

See the step by step solution

Step by Step Solution

Step 1: Calculation for distance of the molecules around you suddenly doubled in volume  (part a)

a.

volume of the space is .

where particles of dust are scattered in.

If we assume a spherical shape.We have ,

The new radius is ,

The radius's dependence on the mean free path, on the other hand, is inversely proportional to its square.

Then the new distance will be,

Substituting the first distance,

Step 2: Calculation for distance of temperature changed (part b)

b.

Volume in number density,

Substitute in the expression for the mean free path, we will have

This means that the distance is proportional to the temperature.

The temperature was increased fromto.

The new line of sight will be,

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