Given: Air is charged into a piston$-$cylinder assembly through a line as shown in the schematic below. A constant force $F=10kN$ and atmospheric pressure of $p_0=100$kPa are exerted on the

piston, whose cross$-$sectional area is $A=0\mathrm{.}05m^2.$ The piston is moving very slowly. The initial air temperature and volume are $T_1=300K$ and $V_1=0\mathrm{.}1m^3,$ respectively. The final air temperature and volume are $T_2=290K$ and $V_2=0\mathrm{.}2m^3,$ respectively. The pipeline pressure and temperature are $p_{\text{l}\text{i}\text{n}\text{e}}=400$kPa and $T_{\text{l}\text{i}\text{n}\text{e}}=300K.$ The piston$-$cylinder is cooled by the surroundings are at $0C.$

Find:

$($a$)$ What is the work performed on the piston by the air in the cylinder, in kJ $?$

$($b$)$ What is the heat transfer during the charging process, in kJ $?$

$($c$)$ What is the total entropy production for the charging process, in $k\frac{J}{K}?$