Answer to Question #164513 in Physics for Saira

Question

Compute the density (in units of m-3) of an ideal gas under the following conditions:

{a) At oC and 760 Torr pressure (I Torr= 1 mm Hg). This is called the Loschmidt number.

{b) In a vacuum of I o-3 Torr at room temperature (20°C). This number is a useful one for the experimentalist to know by heart (10-3 Torr= 1 micron).

Answer 1

a) At 0°C and 760 Torr pressure:

$$n=\frac{P}{k_BT}=2.687·10^{25}\text{ m}^{-3}.$$

b) In a vacuum of 10^-3 Torr at room temperature (20°C):

$$n=\frac{P}{k_BT}=3.286·10^{19}\text{ m}^{-3}.$$