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 α_v, and the coefficient of tension at constant volume α_p, 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 α_A is this absolute coefficient, it defines the absolute temperature as given by the nitrogen thermometer, (since T_B = 1/α_A), and the value of α_A as given by the equation

.

The values of α_A derived from the coefficients of tension, α_p, are found to vary between 0.0036598 and 0.0036628, while those derived from the coefficients of expansion, α_v, vary between 0.0036605 and 0.0036621.