Thermal properties of the high-$T_c$ superconductors ${\mathrm{La}}_{1.85}$${\mathrm{Sr}}_{0.15}$Cu${\mathrm{O}}_4$ and Y${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$

The heat capacity $C_p$ of samples ${\mathrm{La}}_{1.85}$ ${\mathrm{Sr}}_{0.15}$Cu${\mathrm{O}}_4$ and Y${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ has been measured from 1.5 to 40 K, and the linear thermal expansivity $\alpha$ of ${\mathrm{La}}_{1.85}$ ${\mathrm{Sr}}_{0.15}$Cu${\mathrm{O}}_4$ measured in the range 2 to 80 K. The heat capacities show similar temperature dependencies and magnitudes (per gram) with a linear (tunneling?) term dominating below 4 K. $\alpha$ also shows a comparable $T$ term below 4 K and both $C_p$ and $\alpha$ show a small discontinuity of ≈ 1% near $T_c\approx 34$ K.