We have measured the specific heat at constant volume ($C_v$) of ${\mathrm{He}}^4$ near its critical temperature ($T_c$) and critical density (${\rho }_c$). Tabulated data are given along seven isochores with densities in the range $-0.10<\Delta \rho <+0.15\mathrm{}$, where $\Delta \rho =\frac{(\rho -{\rho }_c)}{{\rho }_c}$, at temperatures in the range $-0.06<t<+0.13\mathrm{}$, where $t=\frac{(T-T_c)}{T_c}$. Density resolution was 0.001 ${\rho }_c$ and the resolution of $C_v$ measurements was $0.0003T_c$. in temperature. Resulting values for the critical constants are $T_c=5.1891\mathrm{}\pm 0.0007$ K and ${\rho }_c=0.06958\mathrm{}\pm 0.00007$ g/${\mathrm{cm}}^3$. The data in the one-phase region may be expressed as the sum of a nonsingular function of $t$ and $\Delta \rho$ and a function of the form ${\left|\Delta \rho \right|}^{-\frac{\alpha }{\beta }}f\left(x\right)\mathrm{}$, where $\alpha$ is the exponent describing the singularity in $C_v$ at density ${\rho }_c$ in the one-phase region, $\beta$ is the exponent describing the coexistence curve, and $x$ is the variable suggested in Griffith's discussion of homogeneous functions, $t|{\Delta \rho |}^{\frac{-1\mathrm{}}{\beta }}$ In the two-phase region $C_v$ diverges with an exponent ${\alpha }^{\prime }$ with ${\alpha }^{\prime }\approx \alpha \approx 0.15$. In the two-phase region the singularity in $C_v$ seems to be dominated by $\frac{d^{2}P}{d{T}^2}$ where $P$ is the vapor pressure. If $\mu$ is the chemical potential $\frac{d^2\mu }{d{T}^2}$ is less singular than $\frac{d^{2}P}{d{T}^2}$ and may even be constant in this temperature range. The singularity in $\frac{d^{2}P}{d{T}^2}$ implies the $T_{58}$ helium vapor-pressure temperature scale is slightly in error. If $T_{58}$ and its first derivative are assumed correct at 4.85 K, then $T_{58}$ assigns a temperature 0.0007 K too high to pressures near the critical pressure. Where our $C_v$ data may be compared to $P-V-T$ data on ${\mathrm{He}}^4$ the agreement is generally good. The possibility now exists of making a complete model of the free energy near the critical point.

• Received 6 March 1969

DOI:https://doi.org/10.1103/PhysRev.182.342