A light heat-conducting piston $A$ and a heavy heat-insulating piston $B$ divide the vertical cylinder into two compartments.

Each compartment has a height $L = 40$ cm and there is $1$ mole of an ideal mono-atomic gas in each compartment.Initially, the system is in thermal equilibrium. Then the gas is slowly heated, giving it the amount of heat $Q = 200$ J.

Determine the smallest friction force between piston $A$ and the walls of the vessel at which the piston $A$ remains stationary.

The piston $B$ can move freely without friction.