= Solution
<William Thomson> had to reconcile a successful constraint on engine performance with evidence that mechanical <work> could be converted into <heat>. <Count Rumford>'s cannon-boring observations challenged a finite store of <caloric> by showing sustained production of <heat> through mechanical action. <James Prescott Joule> made the connection quantitative through controlled comparisons of mechanical or electrical input and thermal output. Neither result alone supplied the general limit on converting <heat> back into useful <work>.
Carnot's reversible-engine reasoning supplied that second ingredient, but its conservation-of-caloric interpretation could not simply coexist unchanged with the mechanical equivalent of <heat>. The synthesis retains <energy conservation> while replacing <caloric> conservation: in a cycle, the <heat> received equals <work> produced plus <heat> rejected. A second principle restricts what transformations of that conserved <energy> are possible. In the Thomson formulation, a cyclic device cannot have as its sole result the extraction of <heat> from one reservoir and its complete conversion into <work>. A reversible engine between two <Temperature>[temperatures] sets the <upper bound>; an irreversible one performs worse.
This separation explains why the first law does not imply the second. An imagined perfect converter of <heat> from a single reservoir could conserve total <energy> and still violate the required directionality. Conversely, observing <heat> from <friction> does not prove that every reverse conversion can occur without additional change. Absolute <thermodynamic temperature> gives the reversible comparison an operational scale independent of any particular <thermometer> substance.
Thomson's contribution was a developing reconciliation, not the immediate acceptance of a finished package. Experimental <work>, revised theoretical commitments and collaboration and disagreement with contemporaries all mattered. The resulting laws harmonized work-heat equivalence with limits on cyclic conversion while preserving the useful core, rather than every premise, of Carnot's <argument>.<On the Mechanical Equivalent of Heat by James Prescott Joule>[1850, mechanical work and measured heating]{ref}<Dynamical theory of heat by William Thomson>[1851, fundamental propositions and their relation to Carnot's principle]{ref}
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