Foundational principle: The First Law of Thermodynamics is fundamentally the law of conservation of what quantity?

Introduction / Context:
The First Law of Thermodynamics formalizes energy bookkeeping in closed and open systems, connecting heat, work, and internal energy. It generalizes the conservation principle across mechanical, thermal, and chemical processes.

Given Data / Assumptions:

• Applies to all processes: cyclic, transient, steady state.
• Heat and work are path functions; internal energy is a state function.
• No creation or destruction of energy; only transformations.

Concept / Approach:
The First Law states that the change in total energy of a system equals heat added minus work done by the system. It is a direct statement of energy conservation, encompassing internal, kinetic, and potential energies in engineering analyses.

Step-by-Step Solution:
For a closed system: ΔU = Q − W (ignoring KE/PE).For a steady-flow control volume: ṁ(Δh + Δke + Δpe) = Q̇ − Ẇ_s.Both forms enforce conservation of energy across process boundaries.

Verification / Alternative check:
Energy balances in heat exchangers, compressors, and turbines all instantiate the First Law and show energy is conserved though forms change.

Why Other Options Are Wrong:
Momentum conservation is a mechanics principle (Newton’s laws); mass conservation is separate (continuity). 'None of these' is false because energy is explicit.

Common Pitfalls:

• Confusing heat and work with properties; they are path-dependent interactions.
• Neglecting changes in kinetic/potential energies when significant.

Final Answer:
Energy