Thermomagnetic Gas Torque in Apparatus with Varied Dimensions

Abstract

An axial magnetic field causes a rarefied gas to exert a torque on a heated cylinder $\mathrm{(r)}$ suspended in a gas chamber $\mathrm{(R)}$ . The torque is a peaked function of both $H$ and of $p$ and is related to the Senftleben effect in dilute gases. The direction of the torque is independent of pressure $\text{(0.001\hspace{0.17em}<\hspace{0.17em}p\hspace{0.17em}<\hspace{0.17em}4}\mathrm{torr})$ and of chamber dimensions. The shape $\mathrm{\theta (H)}$ of torque peaks is the same for N₂, CO, and CH₄ and is independent of pressure and of chamber dimensions for $\text{R\hspace{0.17em}/\hspace{0.17em}r\hspace{0.17em}>̄\hspace{0.17em}1.3}$ . The shape is identical to that of the transverse thermal conductivity and wider than that predicted by the volume effect theory of Levi and Beenakker (L–B). The O₂ torque shape is pressure dependent and can be represented accurately as the sum of two component peaks related to the $\mathrm{J\hspace{0.17em}=\hspace{0.17em}K}$ and $\text{K\hspace{0.17em}±\hspace{0.17em}1}$ states of O₂. The position $H_0\mathrm{\hspace{0.17em}/\hspace{0.17em}p}$ of the torque peak is almost independent of chamber dimensions for $\text{p\hspace{0.17em}>\hspace{0.17em}0.05}\mathrm{torr}$ . The size of the torque varies as $\mathrm{(p}\ln {\mathrm{R\hspace{0.17em}/\hspace{0.17em}r)}}^{\text{−1}}$ for $\text{p\hspace{0.17em}>\hspace{0.17em}1.0}\mathrm{torr}$ , in agreement with both volume and surface effect theories. The torque varies as $p^{\text{1.5}}$ for $\text{p\hspace{0.17em}<\hspace{0.17em}0.01}\mathrm{torr}$ . The measured ${\mathrm{p\theta }}_0$ for N₂ above 1.0 torr agrees with the L–B volume effect theory for $\text{R\hspace{0.17em}/\hspace{0.17em}r\hspace{0.17em}=\hspace{0.17em}18}$ but drops to 25% of the theory as $\mathrm{R\hspace{0.17em}/\hspace{0.17em}r}$ is decreased to 1.07 and $\mathrm{(R\hspace{0.17em}-\hspace{0.17em}r)}$ to 1.5 mm. Also for $\text{(R\hspace{0.17em}/\hspace{0.17em}r)\hspace{0.17em}=\hspace{0.17em}1.5}\mathrm{mm}$ , the entire HD torque curve and the O₂ and NO torques for ${\text{H\hspace{0.17em}>\hspace{0.17em}10H}}_0$ reversed direction. These data support the validity of the second‐order Chapman Enskog approximation used in the volume effect theory and suggest that a reverse surface creep flow becomes important for chambers with small wall spacings.