'Heat from Above' Heat Capacity Measurements in Liquid He-4

We have made heat capacity measurements of superfluid He-4 at temperatures very close to the lambda point, T(sub lambda) , in a constant heat flux, Q, when the helium sample is heated from above. In this configuration the helium enters a self-organized (SOC) heat transport state at a temperature T(sub SOC)(Q), which for Q greater than or = 100 nW/sq cm lies below T(sub lambda). At low Q we observe little or no deviation from the bulk Q = 0 heat capacity up to T(sub SOC)(Q); beyond this temperature the heat capacity appears to be sharply depressed, deviating dramatically from its bulk behaviour. This marks the formation and propagation of a SOC/superfluid two phase state, which we confirm with a simple model. The excellent agreement between data and model serves as an independent confirmation of the existence of the SOC state. As Q is increased (up to 6 micron W/sq cm) we observe a Q dependant depression in the heat capacity that occurs just below T(sub SOC)(Q), when the entire sample is still superfluid. This is due to the emergence of a large thermal resistance in the sample, which we have measured and used to model the observed heat capacity depression. Our measurements of the superfluid thermal resistivity are a factor of ten larger than previous measurements by Baddar et al.