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# Variations of pv and p with Temperature

The variations of pv with p at one temperature and the variations of the function pv/T at different temperatures have been investigated recently in the Leiden Laboratory and critically compared with the results of other workers. The compressibilities of oxygen and nitrogen (Amagat, 1893).
The results are best expressed in terms of a power series in which v-1, v-2 are multiplied by coefficients A, B, etc., derived from the experimental results. Graphically the pv values may be plotted against the densities. If the unit of volume is that at 0° C. under 1 atmosphere, and (pv)0 the value of their product under these normal conditions, the deviations with change of volume are as follows: -

At t=0° C. -
(pv)=(pv)0= ; Onnes and v. Urk.
(pv)=(pv)0= . Holborn-Otto.

At t=20° C. -
(pv)=(pv)20= ; Onnes and v. Urk.
(pv)=(pv)20= . Holborn-Otto.

In the following table the values of pv are expressed in terms of (pv)0=1, and the densities "d" in terms of the weight of a normal litre are given at the lowest pressures investigated at each temperature. For the full results the original memoir must be consulted.

 T. (° Abs.). p (Atm.). d. pv. pv/T (T = t+273.09). 293.09 35.84 33.56 1.0680 0.003644 273.09 33.14 33.52 0.9886 0.003620 250.47 33.14 37.13 0.8925 0.003578 222.83 31.98 40.83 0.7833 0.003515 191.99 30.17 46.31 0.6516 0.003394 170.84 28.54 51.185 0.5575 0.003263 151.90 26.63 56.95 0.4675 0.003077 141.72 25.29 60.675 0.4168 0.002933 131.46 23.79 65.76 0.3618 0.002750 128.63 23.20 67.15 0.3455 0.002685 126.77 22.92 68.62 0.3340 0.002634 124.51 27.93 106.06 0.2638 0.002118

The next table gives the change of pv with temperature at a single density of 69 (see table above) between the temperature range of 126.77° and 293.09° C.

 T. (° Abs.). pv. p. 126.77 0.3335 23.01 128.63 0.3427 23.65 131.46 0.3566 24.61 141.72 0.4046 27.92 151.90 0.4508 31.10 170.84 0.5368 37.04 191.99 0.6303 43.49 222.83 0.7644 52.74 250.47 0.8804 60.75 273.09 0.9816 67.73 293.09 1.0670 73.62

Between T=81° and 85° abs., and p=160 and 1326 mm., the pv values are given by the equation

pv =0.27774T - (0.03202 - 0.000253T)p.

The coefficient of expansion at constant pressure αv, and the coefficient of tension at constant volume αp, have been determined by a number of investigators under different pressures between 0° and 100° C. The coefficient at constant volume is numerically the same as the coefficient of tension. These two values t and to a common limit for a perfect gas when the pressure decreases indefinitely, but Regnault showed that equality of the coefficients only occurs at very low pressures.

The coefficient of expansion under limiting conditions of low density and large volume is derived from the actual coefficient under ordinary conditions, combined with a knowledge of the deviation of the actual pv from the absolute (pv)A under the limiting conditions. Thus, if αA is this absolute coefficient, it defines the absolute temperature as given by the nitrogen thermometer, (since TB = 1/αA), and the value of αA as given by the equation .

The values of αA derived from the coefficients of tension, αp, are found to vary between 0.0036598 and 0.0036628, while those derived from the coefficients of expansion, αv, vary between 0.0036605 and 0.0036621.

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