A horizontal cylinder is equipped with a free to move piston.
Gas A with pressure P and volume V is trapped in the cylinder.
The cylinder is then heated and the piston move to the right until the gas expands to twice the volume (2V). What is the pressure now?
I do not know how to do it, but the answer is " the pressure is still P"..
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Well the key words there are 'free to move piston'. If its free to move, and the gas can expand all it wants to. Originally its happy how it is, the pressure is the same inside the piston as outside so it has no reason to expand. Then the heat enters and it expands until the pressure on the outside and inside are again equal. So the pressure has not changed since its the same as the outside pressure and that has not changed.
just remember that in euilibrium, the pressure inside=pressure outside...since pressure ooutside doesnt change in either heated or unheated equilibrium state, the pressure inside doesnt change eiither