Julius von Mayer deduced this statement by intuition, but his poor understanding of physics prevented him from rigorously defining it. When the metric admits a timelike Killing vector field, this statement holds for a particle moving along a geodesic. This statement is equivalent to the argument in Institutions de Physique (“en-stih-too-see-YAWN deh fiz-EEK”) that the living and dead forces have the same measure. The first derivation of this statement is credited to Émilie du Châtelet (“emily doo sha-teh-lay”). The principle of least action as stated by Pierre Louis Maupertuis (“moh-per-TWEEZ”) requires trajectories to obey this statement, but Hamilton’s principle does not. This statement holds when the Lagrangian is invariant under time translations. This statement, which was once at odds with caloric theory, was supported by the measurement of the mechanical equivalent of heat by James Joule. For 10 points, what statement is expressed by the first law of thermodynamics? ■END■
ANSWER: conservation of energy [or energy conservation or descriptions that energy is conserved; accept mass-energy conservation; accept conservation of energy and momentum or energy-momentum conservation; accept first law of thermodynamics until “first law” is read; accept descriptions that energy is converted from one form to another, such as “potential energy is converted into kinetic energy”; prompt on first law until “first law” is read; reject “mass-energy equivalence” or “conservation of mass” or “conservation of momentum”]
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= Average correct buzz position