Using ab initio “data” to accurately determine the fourth density virial coefficient of helium

We combine accurate ab initio calculations of the second and third density virial coefficients, B(T) and C(T), of 4He with measurements of its (p–ρ–T) behavior to determine the fourth density virial coefficient D(T). The measurements were made with a two-sinker, magnetic-suspension densimeter at pressures up to 38 MPa. The measurements on isotherms from T = 223 K to T = 323 K were previously published; new measurements from T = 323 K to T = 500 K are presented here. On each isotherm, a regression of the virial expansion was constrained to the ab initio values of B(T) and C(T); the regression determined D(T) as well as two apparatus-dependent parameters that compensated for systematic errors in the measurements. The percentage uncertainties of D(T) ranged from 2.6% at T = 223 K to 9.5% at T = 400 K to 24.7% at T = 500 K, where these uncertainties are expanded uncertainties with coverage factor of k = 2 corresponding to a 95% confidence interval. These uncertainties are 1/6th of the uncertainty obtained without the ab initio values of B(T) and C(T). The apparatus-dependent parameters can be used to calibrate the densimeter, and this will reduce the uncertainty of other measurements made with this two-sinker densimeter. The new values of D(T) will find applications in accurate gas metrology, such as a primary pressure standard based on the refractive index of helium.