Ideal gasses reaction under const temp and pressure

Conceptual problem:

Let $$A + 2B \rightarrow C + 2D$$ be a reaction under constant pressure ($$P$$) and temperature ($$T$$), that goes all the way towards the products. $$\ce{A,B,C,D}$$ are ideal gases. Let $$\Delta H$$ be the molar enthalpy change in the reaction.

What is the change in the internal energy?

The total amount of moles in the reaction is constant throughout it, can we say that $$\Delta U=\alpha nR\Delta T$$ is the term for the internal energy? (if so that will be 0).

Another idea is that $$PV=nRT \rightarrow V=\textrm{const}$$, and then the internal energy equals the sun of chemical work and heat which we know.

All help appreciated.

as $H=U+PV$ and $PV = nRT=const$ we ger $\Delta(PV)=0 => \Delta U= \Delta H$