E=mc2 Problem Help: Comparing Reactors and Batteries

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The discussion centers on the application of Einstein's equation E=mc² in relation to energy generation in nuclear reactors versus batteries. It highlights that while E=mc² accurately describes mass loss in nuclear reactions, its relevance to chemical reactions, such as those in batteries, is negligible due to the vastly different energy scales involved. Nuclear reactions release energy in the MeV range, while chemical reactions operate in the eV range, making the mass loss from batteries imperceptible. The conversation references Einstein's original work, which indicates that any energy emission or absorption results in a corresponding mass change, albeit minuscule for batteries. Ultimately, the equation is primarily significant for nuclear processes rather than chemical ones.
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the celebrated equation E=mc2 or m=E/c2 (c is the speed of light) tells us how much mass is loss, m, must be suffered by a nuclear reactor in order to generate a given amount of energy, E/ Which of the following statements is correct?

a)The same equation, E=mc2 or m=E/c2, also tells us how much mass loss, m, must be suffered by a flashlight battery when the flashlight puts out a given amount of energy, E.

b) The equation E=mc2 applies to nuclear energy in a reactor, but not to chemical energy in a battery.
 
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Why would either be true? or Why would E=mc2 be true for a nuclear reaction, but not true for a chemical reaction. Nuclear reactions usually involved energies in the MeV range, while chemical reaction energies are in the eV range.
 
Einstein developed E=mc^2 without knowing anything about the nucleus. His paper published in 1905 predated Rutherford's discovery of the nucleus by about six years. In his http://www.fourmilab.ch/etexts/einstein/E_mc2/e_mc2.pdf" , Einstein showed that any object emitting/absorbing light of energy L will lose/gain mass in the amount m = L/c^2. I think that should tell you the answer to the question.

AM
 
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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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