Problem $1($Energy balance for closed system$)$

An unknown ideal gas is contained in a vertical piston$-$cylinder assembly by a piston of mass $40$

kg and having a facial area of $0\mathrm{.}02m^2.$ The mass of the gas is $2\mathrm{.}5$ g $,$ and it initially occupies a

volume of $5$ liters. The atmosphere exerts a pressure of $100$ kPa on the top of the piston. $2$ kJ of

energy is slowly transferred to the gas via heat transfer from a hot plate, and the $($absolute$)$

temperature of the gas increases by $30\%.$ Neglecting friction between the piston and the

cylinder wall, determine the change in specific internal energy of the gas, in $k\frac{J}{k}g.$