Does the first law of thermodynamics univocally define the relative proportions of heat and work?

Does the first law of thermodynamics univocally define the relative proportions of heat and work that are involved

in a given variation of internal energy of a system? Explain.

No. The 1st Law can be expressed as Q-W=deltaU if changes in other state energies such as potential and kinetic are negligible.

So, for a given change in state, there is a fixed value of deltaU. The 1st Law constrains Q and W but does NOT constrain their relative magnitudes. For example, let's say deltaU is 1000 kJ. One path for this change in state could result in Q = 1000 kJ and W = 0 kJ resulting in a ratio of Q/W = infinity. Another path might result in Q = 2000 kJ and W = 1000 kJ. In this case, Q/W = 2. The RELATIVE PROPORTIONS are not constrained by the 1st Law.

No. The first law allows interconversion of heat and work.