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Kapitza resistance is the thermal boundary resistance encountered between a solid and helium in cryogenics. A cold helium heat bath can coexist with a warmer immersed component under continuous heating. The bath's temperature alone therefore does not establish the component's temperature. Kapitza thermal boundary experiment supplied an early direct demonstration of the obstacle at the solid–liquid boundary.

A microscopic route to interfacial heat transfer is transmission of phonons. Transmission depends on the two materials and their interface; scattering and the condition of the surface matter. ^[ref] The fourth-power thermal boundary model isolates one useful low-temperature limiting law without assigning an empirical coefficient to a particular sample.

Pyotr Leonidovich Kapitza's 1941 study suspended cleaned, annealed copper blocks in liquid helium. Sealed, gas-filled cavities held a heater and a bronze resistance thermometer. Electrical readout tracked the heating-induced temperature rise; the earlier readout method assumed a stable bath without a separate bath thermometer. A nearby unheated block warmed much less, localizing the drop near the heated surface. Gold plating and coatings tested surface effects; tight cavities prevented liquid ingress. These were solid-body readings, not probes resolving the microscopic interfacial layer. ^[ref]

The measurement logic suggests a modern control sequence: calibrate both temperature readouts, establish their zero-load difference, increase heater power, wait for a steady state, and repeat while monitoring the bath. Determine lead losses and the bulk temperature gradients before using $r_B=(T_s-T_l)/q$. These are proposed controls derived from the energy balance, rather than additional reported steps in the 1941 apparatus. A nearby unheated solid also has its own interface: its reading need not equal the liquid's local temperature exactly. The experiment supports a drop concentrated near the surface, while a microscopic thickness and a universal interfacial law require further evidence.

Thermal boundary resistance describes a temperature drop between the two sides of a material interface carrying heat flux. Efficient thermal conduction within each material does not guarantee efficient heat transfer between them. The solid–helium case is Kapitza resistance; the broader concept also includes solid–solid interfaces. ^[ref]

Let $T_s$ and $T_l$ be the temperatures extrapolated to the interface from its solid and liquid sides, each treated as internally in thermal equilibrium. For uniform normal heat flux $q>0$ through area $A$, define the finite-drop, area-specific thermal resistance and the resistance of the whole interface byThe macroscopic jump represents an unresolved interfacial region; it is not a claim that one point has two equilibrium temperatures. At nonzero heat flux, the two sides are outside mutual thermal equilibrium. A measured difference between distant thermometers also contains bulk temperature gradients, which must be measured or bounded before assigning all of it to the interface.

An energy balance explains why a temperature jump can coexist with continuous heat flux. For a stationary interfacial region with no local work or heat source,The first law of thermodynamics therefore requires $q_{\mathrm{in}}=q_{\mathrm{out}}=q$ in a steady state. It does not require $T_s=T_l$. For a heated sample with electrical power $P=VI$, an independently determined outward parasitic loss $P_{\mathrm{leak}}$ and no other inputs,Here $V$ is the heater's electric potential difference and $I$ its electric current. Subtracting a lead loss means subtracting power before dividing by area; $q$ is not the total heating power. Unknown losses and stored internal energy prevent that simple steady inference.

For a one-dimensional comparison, put an interface between two slabs with the same area $A$, positive constant thermal conductivities $k_s,k_l$ and lengths $L_s,L_l$. Neglect side losses. Integrating Fourier's law across each slab givesThus, for a linear interface with constant $r_B$, the series result isThese slab formulas are a chosen thermal conduction model, not a bulk transport law for moving liquid helium. If the interface law is nonlinear, substitute its own relation between $q$ and $T_s-T_l$ into the preceding balance; a single constant resistance cannot describe every load. Increasing bulk thermal conductivity has diminishing benefit when the interfacial drop dominates. Increasing usable contact area reduces the whole-interface thermal resistance if the local interface law and the other conditions remain fixed.