The work energy theorem states that the net work on a particle is equal to the change in the kinetic energy of the particle:
$$W_{net}=\Delta K $$
My first question is whether this formula (the work-energy theorem) only applies to single-body rigid systems, that is, whether it only applies to a single particle that cannot be deformed? It is intuitive to me that it should only apply to single-body rigid systems because if the system is not a single-body rigid system, then the system will have the ability to store potential energy and the net work done on the system could lead to an increase in the systems potential energy as opposed to only changing the systems kinetic energy.
My second question is based on the assumption that the work-energy theorem is in fact only true for single-particle rigid systems. If this assumption is true, then is the first law of thermodynamics ( $\Delta U = Q + W $) simply a more general form of the work-energy theorem that can be applied to any system regardless of the amount of particles in the system and regardless of whether they are deformable?
If the first law is a more general form of the work-energy theorem then is my thinking below correct? Suppose we have a system of two particles connected by a spring. Now suppose I apply an external force ( $F_a$ ) on the system over a distance $\Delta x$ (say I give the first particle a push inward toward the second particle compressing the spring but also causing the systems center of mass to move slightly). Since this system is not a single-particle rigid system, we cannot say that $W_{net} = \Delta K$ because the spring compression means the work has lead to an increase in potential energy as well. But $ \Delta U = Q+W $does still apply. And in this case, we clearly have $Q=0$ and also that $W_{net}=F_a \Delta x $ so that we get $\Delta U=F_a \Delta X $ . Now for our system we have that $\Delta U= \Delta V +\Delta K$ . But we do not posses enough information to calculate how much of the work went into increasing the potential energy or went into increasing kinetic energy. All we know for sure is that the change in internal energy equal to the net work done on the system. Is this all correct or am I mistaken?
Any help on this issue would be most appreciated!