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 .
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 ,
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 ,
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,
A mad engineer builds a cube,on a side, in which diameter rubber balls are constantly sent flying in random directions by vibrating walls. He will award a prize to anyone who can figure out how many balls are in the cube without entering it or taking out any of the balls. You decide to shoot diameter plastic balls into the cube, through a small hole, to see how far they get before colliding with a rubber ball. After many shots, you find they travel an average distance of . How many rubber balls do you think are in the cube?
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