Foundational thermodynamics — identifying the law: “The heat and work are mutually convertible.” This statement refers to which law of thermodynamics? Choose the most appropriate law by name.

Introduction / Context:
Thermodynamics organizes our understanding of energy interactions into four numbered laws. The statement “heat and work are mutually convertible” captures the essence of energy conservation when energy crosses a boundary as heat or as work. Correctly mapping such a statement to the appropriate law is essential for engineering analysis.

Given Data / Assumptions:

• Closed or open systems exchanging energy as heat and/or work.
• No chemical reactions are required to interpret the statement.
• Classical (macroscopic) thermodynamics viewpoint.

Concept / Approach:
The First Law of Thermodynamics is an energy balance: the change in total energy of a system equals energy added by heat minus energy leaving as work (plus flow terms for open systems). It formalizes that heat and work are forms of energy transfer and, under proper accounting, one can be converted into the other while conserving total energy. The Zeroth law addresses thermal equilibrium and temperature; the Second law addresses directionality and limits to conversion (entropy); the Third law concerns absolute zero properties.

Step-by-Step Solution:
Identify the key claim: “heat and work are mutually convertible.”Recall the First Law energy balance: ΔE_system = Q_in − W_out (closed system form).Conclude the statement aligns with the First Law’s conservation principle, not with the Zeroth/Second/Third laws.

Verification / Alternative check:
Practical examples—electrical heaters convert work (electric) to heat; steam engines convert heat to work—demonstrate mutual convertibility within energy conservation limits prescribed by the First Law.

Why Other Options Are Wrong:
Zeroth law defines temperature via thermal equilibrium; Second law limits conversion efficiency and introduces entropy; Third law describes entropy behavior near 0 K. None of these state energy conservation between heat and work.

Common Pitfalls:
Confusing “possible to convert” (First Law) with “how much can be converted” (Second Law). The First Law does not guarantee 100% conversion from heat to work; the Second Law limits that.

Final Answer:
First law of thermodynamics