Answer to Question #279276 in Physics for Raymond

Question #279276

Interstellar space far from any star is filled with atomic hydrogen at a density of 1atom/cm at a very low temperature of 273k find




(a) the pressure of the interstellar gas




(b) the root mean speed of the atoms




(c) the edge length of a cube that will contain atoms with a total energy of one joule

1
Expert's answer
2021-12-13T16:55:22-0500

(a) the pressure of the interstellar gas (assuming the temperature is -273°C, or 0.15 K):


p=mRTMV=2.071015 Pa.p=\frac{mRT}{\Mu V}=2.07·10^{-15}\text{ Pa}.

(b) the root mean speed of the atoms:


v=3RT/M=61 m/s.v=\sqrt{3RT/\Mu}=61\text{ m/s}.

(c) Find the edge length of a cube that will contain atoms with a total energy of one joule. 1 m3 is 106 cm3. Each atom has a kinetic energy:


K=12mv2.K=\frac12mv^2.

The number of atoms:


N=E/K=2mv2.N=E/K=\frac{2}{mv^2}.

The number of cubic cm:


V=N.V=N.

The edge of such a cube:


a=V3=N3=1v2m3=1.7444106 cm,a=\sqrt[3]{V}=\sqrt[3]{N}=\frac1v\sqrt[3]{\frac2{m}}=1.7444·10^6\text{ cm},

or 17.444 km.


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