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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.
At t=0° C.  (pv)=(pv)_{0}=; Onnes and v. Urk. (pv)=(pv)_{0}=. HolbornOtto. At t=20° C.  (pv)=(pv)_{20}=; Onnes and v. Urk. (pv)=(pv)_{20}=. HolbornOtto. 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.
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.
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. 
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