By Abello T.P.
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Additional info for Absorption of Ultra-Sonic Waves by Hydrogen and Carbon Dioxide
Given that there are very many molecules in the box, on average, only one-third of them are moving in the x direction; or, better said, only one-third of all components of all velocity vectors are oriented in the x direction. ) For Avogadro’s number, NA , of particles we find, p= 1 mv 2 NA 3 V where v is an unbiased or average particle speed. This is the equation we sought. We already know that pV is an energy and that 12 mv 2 is the kinetic energy of a moving mass m at velocity v. One sees the proportionality in the preceding equation.
This order is pretty much what we would expect from our qualitative knowledge of the three gases. Helium is a “noble” gas, CO2 is commonly available in the condensed state as “dry ice,” and atmospheric N2 is in between. Nitrogen is not as easily driven into the condensed state as CO2 , but liquid nitrogen is far easier to produce than liquid helium. 2 The second virial coefficient of three gases as a function of temperature. Notice the slight maximum in the curve for helium. It is not a computational error, helium really does that.
Please notice the slight change in notation: The y intercept is called y0 , the slope is a, and the quadratic coefficient is b. The general independent variable is x, which is the pressure p in our case. 5341 × 10−5 p 2 where we have truncated the series at the quadratic term. These two exercises make the important point that any data set can be expressed as a collection of numbers (table of observations), a graph, or an analytical equation. Tables, graphs, and empirical equations are merely different ways of saying the same thing.