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A piston is free to move in a cylinder which contains a gas. The gas exerts a force of 10N on the piston, and thus by Newton's 3rd law, the piston exerts a force of 10N on the gas. Hence the gas and piston move in opposite directions, which is contradictory. How do I properly apply Newton's 3rd law to a case like this?

Also, this is completely different from what the intended question, but does the expression $W = PV$ apply to liquids or solids expanding? Does it apply when solids are not expanding, but are being moved, for e.g a cube is physically moved 4 meters by a constant horizontal force of 10N?

Sanjit Sarda
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John
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3 Answers3

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Hence the gas and piston move in opposite directions

No, this statement was too fast. Yes, they both feel the same force, but one force does not give motion. The sum of forces gives motion, according to Newton's 2nd law.

Since the piston is free to move, it moves, but the gas is not free to move since the container-wall behind it holds back. End result is that the net force on the gas is zero and it doesn't move (except for expanding) but the piston with non-zero net force does.

Steeven
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The gas is providing pressure (and thus force). On a microscopic level you have lots of molecules moving in random directions. If there was no piston the gas would expand. Without a wall to supply a force the particles keep on moving. When there is a piston the particles bounce off the wall. Newton's third law applies for every little particle that bounces. The net effect of all these particles bouncing is a pressure. Gasses and liquids apply equal pressure in all directions so the gas is applying pressure to the wall as wel as it self.

The equation $$\Delta W=P\Delta V$$ with $\Delta W$ the work, $P$ the pressure and $\Delta V$ the change in volume holds for all types of materials as long as the change is not too abrupt. Otherwise the pressure can't be defined consistently. This equation is equivalent to $\Delta W=F\Delta x$ but applies to gasses/fluids. You can see this because pressure is force per area: $\Delta W=\frac F A\cdot\Delta x\cdot A=P\Delta V$

AccidentalTaylorExpansion
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Let's consider one molecule that hits the piston. The kinetic energy of that molecule is supplied by breaking a chemical bond during combustion. Just before the molecule hits the piston the molecule's momentum is p = mv, and momentum of piston is p = 0. After the collision the law of conservation of momentum says that sum of momentum must be the same. Hence, as molecule bounce back with new momentum, the piston moves forward with some new momentum GREATER than zero. Hence the piston movement. With many of molecules hitting the piston it can move and produce useful work. For piston as a system the force comes from the molecule as external force and in accordance to Newton's Second Law piston will accelerate.