Thermodynamic Basis — What Fundamental Law Do Steam Engines Rely On? All steam engines (prime movers converting heat to work) fundamentally operate in accordance with which law of thermodynamics?

Introduction / Context:
Steam engines convert thermal energy of steam into mechanical work using a thermodynamic cycle. While all physical processes must obey energy conservation (first law), the directionality and limits of heat-to-work conversion are governed by the second law. Recognizing this distinction is essential for understanding why no engine can be 100% efficient.

Given Data / Assumptions:

• Heat engine operating between a hot reservoir (boiler) and a cold reservoir (condenser/ambient).
• Cycle includes expansion doing work and heat rejection.

Concept / Approach:
The first law states energy conservation: Q_in − Q_out = W_net. However, it does not restrict the fraction of heat that can be converted to work. The second law introduces entropy and the necessity of heat rejection; it establishes that complete conversion of heat into work in a cyclic process is impossible and sets the theoretical efficiency ceiling via the Carnot limit. Therefore, the very possibility and limitation of a heat engine depend on the second law.

Step-by-Step Solution:
Identify engine as a heat engine: requires a temperature difference.Apply first law: balances energy but allows, in principle, any efficiency if taken alone.Apply second law: dictates irreversibility and that some heat must be rejected; efficiency is fundamentally limited.Hence, steam engines “work on” (are constrained by) the second law.

Verification / Alternative check:
Ideal Rankine/Carnot analyses show that as sink temperature approaches source temperature, efficiency tends to zero, a direct consequence of the second law.

Why Other Options Are Wrong:

• Zeroth law: defines temperature and thermal equilibrium, not engine operation.
• First law: necessary but not sufficient to explain direction and limits of conversion.
• None: incorrect because thermodynamic laws govern all heat engines.

Common Pitfalls:
Attributing engine feasibility solely to energy conservation; without the second law, perpetual heat-to-work conversion would not be prohibited.

Final Answer:
Second law of thermodynamics