First Law for a Closed System – Choose the Correct Statement Which of the following correctly expresses the First Law of Thermodynamics for a closed system over a process from state 1 to 2?

Introduction / Context:
The First Law of Thermodynamics is the statement of energy conservation for thermodynamic systems. For closed systems, it relates heat transfer, work, and the change in total energy (internal, kinetic, potential). Selecting the correct form avoids many conceptual mistakes in problem solving.

Given Data / Assumptions:

• Closed system (fixed mass) undergoes a process from state 1 to state 2.
• Sign convention: heat added to the system positive; work done by the system positive.
• Total energy E includes U + KE + PE unless stated negligible.

Concept / Approach:

The general First-Law statement for a closed system is ΔE = Q − W. In words: the increase in system energy equals the net heat added minus the work done by the system. Special cases (adiabatic, isochoric, cyclic) are all contained within this master equation by setting appropriate terms to zero.

Step-by-Step Solution:

Verification / Alternative check:

Control-mass piston–cylinder analyses and calorimetry experiments consistently validate ΔE = Q − W across diverse processes when all energy contributions are accounted for.

Why Other Options Are Wrong:

(a) Internal energy is not constant in general; (c) is only true for ΔE = 0 cases; (d) incorrectly groups properties—entropy is not conserved in irreversible processes and enthalpy is path-dependent except in special cases; (e) is false because heat and work are path functions, not state properties.

Common Pitfalls:

Mixing sign conventions, neglecting kinetic/potential energies when they matter, and assuming cyclic identities apply to noncyclic processes.

Final Answer:

The total energy change equals heat added minus work done: ΔE = Q − W.