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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} ##?