## 3 Interfacial Thermal Resistance at the Membrane/Gas Interface  
Let us consider the change in the gas temperature near the hot zone of the membrane at distances comparable to \(l_{mfp}\). Note that for distances of the order of \(l_{mfp}\), it is necessary to clarify the concept of the gas temperature. Temperature is commonly defined as the average local energy of gas molecules, assuming that the distribution function is the same as for large volumes [28]. Consider the temperature jump \(\Delta T_{C}\) at the membrane/gas contact. This jump in temperature means that there is a contact thermal resistance at the interface between the gas and the calorimeter membrane. In this case, the so-called temperature jump distance \(\delta\) can be introduced [29; 30]. In fact, the effect of the temperature jump increases the length of the heat transfer path through the gas by an amount of \(\delta\), which is of the order of \(l_{mfp}\). Usually, the boundary condition that takes into account the temperature jump at the membrane/gas interface is represented by Equation (1) [29; 30]:  
\[T_{K}-T_{m}=\delta\frac{\partial T}{\partial z}, \tag{1}\]  
where \(T_{m}\) is the temperature of the membrane, and \(T_{K}\) is the gas temperature extrapolated to the membrane, as if the temperature gradient in the gas \(\frac{\partial T}{\partial z}\) was not distorted due to the temperature jump at the interface. The temperature jump distance \(\delta\) depends on the following gas parameters: mean free path \(l_{mfp}\), heat capacity ratio \(\gamma\), kinematic viscosity \(\
u\), and thermal diffusivity \(D=\lambda/\rho c_{p}\), where \(\rho\) and \(c_{p}\) are the density and specific heat capacity at constant pressure, respectively. The temperature jump distance \(\delta\) can be represented by Equation (2) [29; 30]:  
\[\delta=\left(\frac{2-\sigma}{\sigma}\right)\left(\frac{2\gamma}{1+\gamma} \right)\left(\frac{\lambda}{\
u c_{p}}\right)l_{mfp}, \tag{2}\]  
where \(\sigma\) is the thermal accommodation coefficient in the boundary condition, see Equation (3). \[T_{r}=\sigma T_{m}+T_{i}(1-\sigma), \tag{3}\]  
where \(T_{i}\) and \(T_{r}\) are the temperatures of the incident and reflected gas molecules; \(T_{m}\) is the membrane temperature [29; 30]. In fact, \(\sigma\) denotes the fraction of molecules that are diffusely reflected from the membrane at the temperature \(T_{m}\). The remaining fraction of moleculesis reflected specularly, which means that their velocity components, perpendicular to the membrane surface, only change sign. Thus, it follows from Equation (3) that \(\sigma\) can be represented as:  
\[\sigma=(T_{r}-T_{i})/(T_{m}-T_{i}). \tag{4}\]  
Equation (4) reveals the physical meaning of the thermal accommodation coefficient \(\sigma\). The parameter \(\sigma\) depends on the gas molecules and the solid surface with which the gas molecules interact. This parameter becomes close to 1 for a blackened surface [30]. \(\sigma\) is relatively small for light gas molecules. For example, for helium gas and bright platinum \(\sigma\) is about 0.5, and 0.9 for blackened platinum [30]. However, for CO\({}_{2}\) gas, \(\sigma\) is about 1 for various solids [30]. Let us consider the thermal contact conductance \(G_{C}\) at the membrane/gas interface. By definition, the thermal contact conductance \(G_{C}\) is equal to the ratio \(q_{C}/\Delta T_{C}\), where \(q_{C}\) is the heat flux through the interface [30]. \(q_{C}\) is equal to the product of \(\lambda\) and the temperature gradient in the gas near the interface. \(\Delta T_{C}\) is equal to the product of \(\delta\) and the temperature gradient in the gas near the interface. Thus, the thermal contact conductance \(G_{C}\) is:  
\[G_{C}= \lambda/\delta. \tag{5}\]  
[PERSON] calculated the energy flux \(G_{max}(T-T_{t})\) from a unit area of a solid in a gas at a constant pressure \(p\), which is the maximum possible heat flux at the solid/gas interface [29; 31].