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CGandC
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Homework Statement
Suppose there is a tank filled with water and a piston of area S exerts a force F on the water.
Suppose I divide the water boundary touching the piston to - N small equal " square " molecules.
Then , the force on the upper face of each molecule is F/N .
Also, the area of the upper face of each molecule is of length S/N .
Thus , the pressure on each molecule touching the piston is : ## P = \frac{F/N}{S/N} = \frac{F}{S} ##
And this is the same pressure that each molecule exerts on the piston
Question: If ## P = \frac{F}{S} ## is also the pressure that each molecule ( touching the piston ) exerts on the piston, then , if I sum the pressures exerted by each such molecule on the piston, I get:
## P = \frac{F}{S} + \frac{F}{S} + ... + \frac{F}{S} = \frac{N*F}{S} ##
which contradicts conservation of energy and also because it just seems wrong because I was told the pressure on the piston is just : ## P = \frac{F}{S} ## and not ## P = \frac{N*F}{S} ##
Why is there contradiction of conservation of energy and why the pressure on the piston is not ## P = \frac{N*F}{S} ##?