During the explanation of Pascal's law the argument that work done by a force to move the fluid inside communicating vessel is equal to the work done by the fluid at the other end of the vessel was used to prove that pressure everywhere is the same.

I am wondering whether it is strictly necessary that work input must be the same as work output. What if we convert some energy from the work we put in to heat or something else and convert the remainder to work output. By this we are not even violating the requirement that the displacement of piston at one end of vessel is necessary if the fluid (incompressible) has been pushed from the other end. If this can be done the pressure at two ends of the vessel will not be equal - thus violating Pascal's law.

Why is the conversion of work input into something other than work output (apparently) not possible?


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