The figure shows two compartments separated by a thin wall. The left side contains $0\mathrm{.}06$ mol of helium at an initial temperature of $600$ K and the right side contains $0\mathrm{.}03$ mol of helium at an initial temperature of $300$ K $.$ The compartment on the right is attached to a vertical cylinder. A $11$ cm diameter, $2$ kg piston can slide without friction up and down the cylinder. The volumes of the compartments are unknown. The exterior pressure is $0\mathrm{.}9$ atm $.$

$($A$)$ What is the final temperature?

$T=$

K$.$

$($B$)$ How much heat is transferred from the left side to the right side? $($The heat lost on the left is equal in magnitude to the heat gained by the right.$)$

$Q_2=,J$

$($C$)$ What is the change in height of the piston after being lifted due to this heat transfer?

$y=,m$

$($D$)$ What fraction of the heat is converted into work?

$\frac{W_2}{Q_2}=$