Heat definition in isotherm and first principle of thermodinamic We know that the heat Q can be computed by $Q=cm\Delta T$ and in a phase change by $Q=Lm$ (L latent heat).
In isotherm process and with no change of phase we can't use those formulas and there's no formula for defintion of Q (correct me if I'm wrong). Usually we use $\Delta U=Q-L$ but so we are defining Q by the first principle and so in isotherm process the first principle is more a definiton that a principle.
Is this observation correct?
 A: 
In isotherm process and with no change of phase we can't use those
  formulas and there's no formula for defintion of Q (correct me if I'm
  wrong).

You are correct that you can't use those two formulas for an isothermal process with no phase change, but you can determine $Q$ from the first law. 

Usually we use $\Delta U=Q-L$ but so we are defining Q by the first
  principle so in isotherm process the first principle is more a
  definiton that a principle. Is this observation correct?

The first law for a closed system is not your equation which uses latent heat, but the following: 
$$\Delta U=Q-W$$
Where $Q$ is heat and is positive if added to the system, and $W$ is work and is positive if done by the system. The first law is  not a definition of heat, but relates heat and work to changes in internal energy. 
For an ideal gas undergoing an isothermal process ($\Delta T=0$, and $Pv=$ constant),$\Delta U=0$ because $\Delta U=mC_{v}\Delta T$ for any process. Therefore, for an ideal gas $Q=W$, which is to say that the heat added (or removed) from the system exactly equals the work done by (or on) the system. For an ideal gas that work would be:
$$W=RTln\frac{v_2}{v_1}=RTln\frac{P_1}{P_2}$$
Where 2 and 1 denote final and initial values, respectively, of pressure and volume.

And if I have no choice I think that in this case the first law is a
  definition of heat. Suppose a beginner student, without knowing the
  first law, ask to you how the heat is defined in a rigorous way in
  that 'case of no choice' what definition you give to him if you can't
  use first law?

I would first give the student the overarching general thermodynamics definition of heat:
HEAT: Energy transfer between a system and its surroundings due solely to a temperature difference between them.
I would then point out that the emphasis in thermodynamics is the effect of heat transfer on the properties of substances (temperature, internal kinetic and/or potential energy, phase changes, etc.) and the applicable equations as we have been talking about in this post. 
But I would also point out that although in thermodynamics we often don't need to worry about the exact mechanism of the heat transfer (conduction, convection, radiation) one or more of those mechanisms has to be involved, and there are well defined laws and equations for each mechanism. For example we have (1) Fourier's Law of Conduction (for conduction), (2) Newton's Law of Cooling (for convection), and (3) Stephan-Boltzmann law of thermal radiation (for radiation), and the associated equations for each. 
In our example of the isothermal process for an ideal gas we didn't need to know about the heat transfer mechanism involved. It was sufficient to know the heat transfer equals the work. But if we wanted to know the laws governing the heat transfer mechanism, there are such laws and associate equations, depending on which mechanism(s) is (are) involved.
Hope this helps.
