Heat-capacity study of the second layer ofHe3adsorbed on Grafoil

Heat-capacity measurements on adsorbed ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ are reported. The densities studied start slightly under monolayer completion and go up to slightly above second-layer completion. The temperature range is $0.04 \mathrm{K}<T<\mathrm{}4.2\mathrm{} \mathrm{K}$. After subtraction of calculated values of the contributions from the first layer (solid), and desorption, we find that the second layer behaves as a two-dimensional interacting Fermi gas at all densities for which a partial third layer is not present. The second-layer gas cannot be represented by the same second virial coefficient used for the first layer. The absence of the substrate-induced ordering transition allows one to study the gas behavior over a larger range of densities than on the first layer. We find that the shape, temperature, and density dependence of the very low temperature (∼ 0.1 K) rounded anomaly in the specific heat is different than on the first layer. With a very small amount of third layer present, the second layer solidifies for temperatures below 0.98 K.