00:01
So we're told that the number density of hydrogen atoms in sort of the interstellar medium is about one atom per cubic centimeter.
00:12
And we're told that the temperature of the interstellar medium is about 3 kelvin.
00:17
And so from this information, we want to know what is the pressure in interstellar space.
00:23
So the pressure, we can write it using the ideal gas law, pv equals nkt.
00:29
It's boltzman's constant this is the number of atoms so if we divide by the volume what we get is like the number density you know n divided by v is going to be lowercase n times boltzman constant times the temperature so in is capital n over v so this number density comes out to about if cubic meters this is about a million hydrogen atoms per cubic meter and so if we plug in some of these numbers, what we have is a million, sorry, per cubic meter.
01:09
So a million atoms per cubic meter times bolton's constant, which is 1 .38 times 10 to the negative 23rd, joules per kelvin times 3 kelvin.
01:21
This comes out to a very small number, about 4 .14 times 10 to the negative 17th pascal's.
01:31
And in terms of atmospheres we divide by 101 ,350 so if we do this this is about 4 .08 times 10 to the negative 22nd atmospheres so very very very very small and then from here we want to find what's the root mean square velocity so in terms of the temperature root mean square velocity is like 3 k t over m and so the m we're going to use is basically the mass of a proton because a hydrogen atom, the mass is almost entirely from the proton, and so it's a good approximation.
02:08
So this is 3 times 1 .38 times 10 to the negative 23rd, joules per kelvin, times 3 kelvin.
02:17
The mass of a proton is 1 .6 times 10 to the negative 27th kilograms.
02:23
And if we plug in all our numbers right, we get about 278 meters a second, which is still, you know, kind of fast.
02:30
And then lastly, we want to know what volume is required, or what's the length of a cube, the side length of a cube, required so that the energy density of that cube is just one jewel.
02:44
So basically, if we fit one jewel into a cube, how small does a cube have to be? one jewel of thermal energy from these atoms...