Barometer formula

Formula (4.1) is often called the barometer formula, since it gives the variation of barometric pressure with altitude. It indicates a gradual decrease of pressure with altitude, going exponentially to zero at infinite height. 

The barometer formula can be derived by elementary methods, thus checking this part of the Maxwell-Boltzmann distribution law. Consider a column of atmosphere 1 sq. cm. in cross section, and take a section of this column bounded by horizontal planes at heights ft and ft + dh. Let the pressure in this section be P we are interested in the variation of P with ft. Now it is just the fact that the pressure is greater on the lower face of the section than on the upper one which holds the gas up against gravity. That is, if P is the upward pressure on the lower face, P + dP the downward pressure on the upper face, the net downward force is dP,... 

The derivation which we have given for the barometer formula in Eq. (4.3) can be easily extended to a general potential energy. Let the potential energy of a molecule be . Then the force acting on it is d/ds, where ds is a displacement opposite to the direction in which the force acts. Take a unit cross section of height ds in this direction. Then, as before, we have... 

The student quickly scribbled, Take the barometer and a stop watch to the top of the building and lean over the edge of the roof. Drop the barometer and measure the duration of its fall with the stop watch. Then using the formula S = 1/2 a t2 to calculate the height of the building. The arbiter showed the answer to his colleague and the student received almost full credit for this answer. 

An example will make the formula more intelligible. A student actually found that a mixture of potassium chlorate and manganese dioxide yielded 2192.4 cc. of oxygen when the barometer read 757.8 mm. and the ther-... 

Bakker s theory of capillarity, 206 balancing cplumns apparatus, 12, 36 balls, for viscometer, 87 barometer tube method, 228 Batschinsky s formulae, 90 Baum6 s scale, 15... 

When a distillation is performed at atmospheric pressure it is necessary to take several readings of the barometric pressure. Variations of 20 mm in the reading can, for instance in the case of benzene, give rise to differences in the boiling point of 1 deg. C. The barometer should be checked against a precision instrument and a correction should be applied for the influence of temperature on the mercury column and the scale. This can be done without calculation by means of a nomogram due to Haussler [240] (Fig. 114). It is based on the formula... 

The following corrections are used to reduce the reading of a mercury barometer with a brass scale to 0°C. The number in the table should be subtracted from the observed height of the mercury column to give the true pressure in mmHg (ImmHg = 133.322 Pa). The table is calculated from the formula... 

Based on the values in the formula the least number of significant figures is five so we need to round off R to five significant figures as 0.082057 (L atm/°K mol). We note that 22.414 L is about the size of a 5 gal solvent can and we need to tabulate some key unit facts in this first chapter. At this point it is easy to introduce the SI equivalent of the gas constant since the only difference is that the pressure is measured in bars where 1 atm= 1.01325 bar. (Note that a barometer measures bars.) However, at the lower pressure the molar volume will be larger at about 22.711 L ... 

Solution To find the solution we have to use the barometric height (bh) formula (refer to Section 3.2.2). The barometer can show constant pressure p at various temperatures to T2 onboard only in the case where the plane is not at height h (which the pilot counts constant), but at some other height Write the barometric height formula (3.2.7) for these two heights ... 

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