Abstract
We observe a thermomechanical effect when a chemical-potential difference is created by a temperature difference imposed between two liquid reservoirs connected to each other through Vycor rods in series with solid hcp $^{4}\text{H}\text{e}$. By creating a temperature difference, $\ensuremath{\Delta}T$, between the two reservoirs, we induce a rate-limited growth of a pressure difference between the two reservoirs, $\ensuremath{\Delta}P$. In equilibrium $\ensuremath{\Delta}P$ vs $\ensuremath{\Delta}T$ is in quantitative agreement with the thermomechanical effect in superfluid helium. These observations confirm that below $\ensuremath{\sim}600\text{ }\text{mK}$ a flux-limited flow exists through the solid helium.
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