# The force acting on a piston in a gas canister and the movement of the piston

I apologize if this question is too simple to ask but I'm not entirely sure about the mistake that I'm making and I honestly would appreciate the help.

In the cylinder of a vehicle ($$r=5$$cm, resting state $$l=7$$cm) a gas mixture is heated from room temperature (at $$273K$$) to $$1000^\circ C$$. The initial pressure is $$1$$ bar.

1.What is the force acting on the piston due to the pressure in the cylinder if the piston is fixed.

2.How far does the piston move if no other external forces are acting on it (Except the atmospheric pressure $$p$$

If I'm not mistaken the answer to the first question should simply be the pressure force of the gas? I start with the ideal gas law $$PV=nRT$$ and because the the shape of the cylinder the area of the piston and the volume should be $$A=\pi r^2$$, $$V=\pi r^2l$$ then by the definition of pressure $$PV=\frac{F}{A}V=nRT \implies F=A\frac{nRT}{V} \implies F=\frac{nRT}{l}$$

For the second question I observe how the equation changes. I set the initial conditions as $$(100000)(\pi)(5)^2(7)=(8.3145)(273)n$$ From here I find $$n=24220$$. Then I assume that after the heating the number of moles won't change so the right hand side of the equation stays the same and only the pressure and the volume changes. I assume once the piston reaches equilibrium the pressure inside will be equal to the atmospheric pressure so the second equation is $$10^5V'=(24220)(8.3145)(1273).$$ Since the radius won't change after the heating $$V'=\pi r^2l'$$ therfore $$l'=\frac{(24220)(8.3145)(1273)}{(10^5)(5^2 \pi)}$$ which is $$l=32.6$$ but I'm fairly sure that a piston can't move 36cm vertically in a canister that is only 7cm long vertically but I went over my work several times and can't find a mistake.

• Hint: The release process should be assumed to be adiabatic. Commented Jan 11, 2022 at 14:50
• Note that the question does not state the length of the canister. It only states that in the "resting state", the piston is l = 7cm from the top. The canister could be 1 m long, for all we know. That is how I read the definition of l, and how you have used that definition as well. Commented Jan 11, 2022 at 15:23