Answer to Question #279276 in Physics for Raymond

Question

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

Answer 1

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

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

(b) the root mean speed of the atoms:

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

(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:

$$K=\frac12mv^2.$$

The number of atoms:

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

The number of cubic cm:

$$V=N.$$

The edge of such a cube:

$$a=\sqrt[3]{V}=\sqrt[3]{N}=\frac1v\sqrt[3]{\frac2{m}}=1.7444·10^6\text{ cm},$$

or 17.444 km.