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Mathematics
General Math
How to compute the energy needed to compress the water isothermally?
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[QUOTE="I like Serena, post: 6782402, member: 312166"] Your expert's answer assumes that the force/pressure is constant at 100 atmosphere, but that is not the case. Instead it will build up from 1 atmosphere up to 100 atmosphere. So we can expect the actual answer to be about half of that $506\,J$, which is really an upper estimate. I found $229\,J$ myself while taking the changing pressure into account with Calculus, which is indeed in the neighborhood of half of that $506\,J$. Either way, it looks as if the answer of $29.4\,J$ is not correct. We take the coefficient of isothermal compressibility of water at $20^\circ C$. [URL='https://en.wikipedia.org/wiki/Properties_of_water#Compressibility']Wikipedia[/URL] mentions that it is $4.4$ to $5.1×10^{-10}\, Pa^{-1}$ in ordinary conditions. Close enough to that 46.4 parts per million that you mentioned. [/QUOTE]
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How to compute the energy needed to compress the water isothermally?
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