By Christopher J. Foot
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Calculate its mass at the same pressure but at 10 ◦ C and 20 ◦ C. 2 Calculate the mass of a 1 m3 parcel of water vapor at STP. 3 What is the partial pressure of oxygen in a dry 1 m cube of air at STP? 4 What is the weight of the 1 m cube of dry air at STP? In newtons, in pounds? 5 What is the number density of a volume of pure oxygen (O2 ) at STP? 6 Express Rd in terms of hPa instead of Pa. 7 Use dP(v)/dv = 0 to ﬁnd a formula for the most probable speed of a molecule at STP. 8 Compute the vrms for O2 , N2 , Ar, and H2 at STP.
The coefﬁcient of proportionality is thus determined to be 32 times the Boltzmann constant. Note that when the absolute or Kelvin temperature T is zero, the molecules are at rest (v02 = 0). All thermal motion is presumed zero at this temperature at least in the ideal gas as we have deﬁned it. Actually, there is no such thing as an ideal gas at 0 K (any real gas would have been liquiﬁed or solidiﬁed well above 0 K). Moreover, quantum mechanics tells us that there is motion even at this lowest of low temperatures.
The maximum surface temperature on the Moon is about 400 K. 8 shows the distribution of speeds for this case. 73 ×10−7 , easily large enough for the Moon to lose its atmosphere over its lifetime. 8 The distribution of molecular air molecules for the Moon at 400 K. The escape velocity is 2380 m s−1 . 3 Flux of molecules striking a wall There are many derivations of elementary processes in kinetic theory. We present one more here since the result comes up often. We want to know the number of molecules striking a wall (perpendicular to the x-axis) per unit time and area.