thermodynamics - Why internal energy in Lagrangian is treated as a potential energy?

To obtain Euler fluid equations of motion one can do variational principle on the following Lagrangian density where $\rho_0$ is reference density, $\Phi$ is displacement vector field and $u$ is internal energy density.

$$ \mathcal{L} = \frac{1}{2}\rho_0 \left( \frac{\partial \Phi}{\partial t} \right)^2 - \rho_0 u $$

This model (Euler fluid + thermodynamics) is supposed to work for ideal gas as well. For that we know that internal energy is assumed to be consisting only of average kinetic energy of individual gas particles. But we know that in inertial reference frame Lagrangian has the following form where $K$ is kinetic energy density and $U$ is potential energy density.

$$ \mathcal{L} = K - U $$

How to explain that even though internal energy is average kinetic energy, in Lagrangian it is with negative sign which can be interpreted as internal energy being potential energy of some sort?