No, the internal energy of a system is not frame dependent. The internal energy of a system refers to the total energy associated with the microscopic components of the system, such as the kinetic energy of the particles and the potential energy associated with their interactions. It is a property of the system itself and is independent of the frame of reference or the observer.
The internal energy depends on the state of the system, which is determined by its thermodynamic variables such as temperature, pressure, and composition. These thermodynamic variables define the internal energy, regardless of the reference frame or observer.
However, it's important to note that the measured values of temperature and other thermodynamic variables can depend on the reference frame or observer if there are relativistic effects at play. In such cases, the relationship between temperature and other variables may be affected by the relative motion between the observer and the system. But the internal energy itself, which is the sum of the microscopic energies within the system, remains frame independent.