Is E = E(in) - E(out) + E(generated) a valid expression for energy conservation?

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The expression E = E(in) - E(out) + E(generated) is presented as a form of energy conservation, specifically in the context of heat conservation. It outlines the balance of energy entering, leaving, and being generated within a system. While this formula captures a specific scenario, it may not represent a general law of energy conservation applicable in all contexts. The discussion references a more comprehensive approach to energy conservation by Jewett Jr., emphasizing that energy conservation principles can vary based on the system analyzed. Overall, the expression serves as a useful tool for understanding energy flow in specific cases rather than a universal law.
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Hello,

I nowhere find general form of energy conservation law, but in one book i found this

(*)\hspace{1cm}E=E_{in}-E_{out}+E_{generated}

where E(in) is energy flow into system, E(out) is energy flow out of system and E(generated) is energy generated. It was in sense of heat conservation. Can I use this form of heat conservation law? Or is it true, when I say, (*) is energy conservation law?
 
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Jewett Jr. has actually presented a somewhat "global energy conservation equation" in Energy and the Confused Student IV: A global approach to energy (Phys. Teach. 46, 210 (2008)). You can access it here: http://dx.doi.org/10.1119/1.2895670
 
It is a simple concept, it does not require mathematics to understand. What you wrote up there looks like the energy conservation principle applied to a control volume in some particular case.

If you are just looking for a formula to plug and chug at, you won't find it. Not that it would be useful anyways.
 
For simple comparison, I think the same thought process can be followed as a block slides down a hill, - for block down hill, simple starting PE of mgh to final max KE 0.5mv^2 - comparing PE1 to max KE2 would result in finding the work friction did through the process. efficiency is just 100*KE2/PE1. If a mousetrap car travels along a flat surface, a starting PE of 0.5 k th^2 can be measured and maximum velocity of the car can also be measured. If energy efficiency is defined by...

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