Some Physical Properties of Compressed Gases. I. Nitrogen

The writers have adjusted and extrapolated the compressibility data obtained by Bartlett and his collaborators on nitrogen, so that very accurate p-v-T data from --- 70 to 600^∘{} and up to 1200 atm. are available. A suitable graphical scheme has been devised for obtaining the derivatives (dv/dp)T, (dv/dT)ₚ, (d²vdT²)ₚ at any point in order that some of the physical properties of the gas can be calculated. This graphical scheme depends on the relation of α≡RTp-v and Δ≡v(pv/RT-1) to p, v, T, and on the relations of the derivatives of α and Δ to the derivatives of v. Errors in the estimation of the slope of an α or Δ curve at any point introduce much smaller errors into the derivatives of v, since the derivatives of α and Δ enter as correction terms to the derivatives of v just as α and Δ are corrections to v itself.A graphical process is used as originally in MS for adjusting the p-v-T data and all the physical properties derived from it. This process is based on the assumption that surfaces such as p-v-T; α-v-T; or Δ-v-T are smooth and hence that the curves in any family of isotherms or isobars show related characteristics. It throws most of the adjustment on v, where it belongs, since the measurements of p and T are much more accurate than those of v. Such an adjustment enhances the precision of the compressibility data and of the calculations made from it.The specific volume, density, coefficients (-p/v)(dv/dp)T and (T/v)(dv/dT)ₚ, fugacity, Cₚ, Cₚ-Cᵥ, Cᵥ, and μ are calculated and shown in curves and a table for the fourteen pressures and twelve temperatures in the range studied. Inversion pressures and temperatures are read from the μ vs. p isotherms and the μ vs. T isobars.The calculations of Cₚ agree well with the experimental values of Krase and Mackey, who worked at 30, 100, 125, 150^∘{} up to 700 atm. and at 50^∘{} to 800 atm. The agreement is probably within the experimental error, but the trends of the two sets suggest that a real difference may exist. At 30^∘{} the calculated Cₚ drift below the experimental values at pressures above 400 atm., becoming 0.13 cal/mole·{}deg low at 700 atm. At 50^∘{} the agreement is good to 800 atm. At 100, 125, 150^∘{} the calculated Cₚ drift above the experimental values, but the disagreement reaches only 0.2 cal/mole·{}deg at 600 and 700 atm.As one might expect, Cₚ-Cᵥ approaches R at all temperatures as the pressure approaches zero. In general, Cₚ-Cᵥ increases at any particular pressure as the temperature decreases. Cₚ-Cᵥ shows a strong maximum at about 200 atm. at the lowest temperatures. With increasing temperature this maximum comes at higher and higher pressures, and gradually disappears. The Cᵥ vs. T isobars show some curious tendencies. Cᵥ along the 20 atm. isobare stays constant and equal to 2.50 R from -70 to 100^∘{}C, then it rises slowly to 5.15 cal/mole·{}deg at 600^∘{}. Along the 40, 60, 80, and 100 atm. isobars, Cᵥ drops a few hundredths of a cal/mole·{}deg below 2.50 R at -70^∘{}. the drop being greater the greater the pressure. Along the 200 atm and higher pressure isobars, Cᵥ rises as the temperature falls below 50^∘{}, and the rise is steeper the greater the pressure. At 600^∘{} Cᵥ is about 5.18 cal/mole deg or 2.61 R for all pressures.