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Q. 42

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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

Interstellar space, far from any stars, is filled with a very low density of hydrogen atoms ,not. The number density is aboutand the temperature is about .

a. Estimate the pressure in interstellar space. Give your answer in and in .

b. What is the rms speed of the atoms?

c. What is the edge lengthof ancube of gas withof thermal energy?

a. Pressure in interstellar space inisand in is .

b. RMS speed of atom is.

c. Edge length is .

See the step by step solution

Step by Step Solution

Step 1: Calculation of pressure inand(part a)

a.

The number density is,

Ideal gas law is given by ,

Where is Boltzmann's constant .

In unit its value is,

The number of density is ,

.

The values ofand into equationto getin

Pressure of atom in ,

Step 2: Calculation for root mean square speed (part b)

b.

The average translational kinetic energy is,

As shown, both equationsandhave the same left side,

Use these expressions to get an equation for root mean square velocity,

The mass of the hydrogen atom is the same for the proton is, .

Substitute the values for, and into equation to get ,

Step 3: Calculation for length (part c)

c.

Translational kinetic energy is the kinetic energy of a monatomic gas.

Where is the number of particles

is the universal gas constant.

The volume is given by .

So, the number of molecules is,

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