A vertical $10-$cm$-$diameter piston$$cylinder device contains an ideal gas at the ambient conditions of $1$ bar and $24$C$.$ Initially, the inner face of the piston is $20$ cm from the base of the cylinder. Now an external shaft connected to the piston exerts a force corresponding to a boundary work input of $0\mathrm{.}1$ kJ$.$ The temperature of the gas remains constant during the process. Determine $($a$)$ the amount of heat transfer, $($b$)$ the final pressure in the cylinder, and $($c$)$ the distance that the piston is displaced.