$HW-6(i)$

A gas $(m=0\mathrm{.}004kg)$ is contained in a closed, vertical piston$-$cylinder

device; mass of the piston is $50$ kg and the area of the piston is $0\mathrm{.}01m^2.$

Assume that atmospheric pressure of $100$ kPa acts outside the piston and

acceleration due to gravity is $9\mathrm{.}81\frac{m}{s^2}.$ The gas has an initial volume of

$0\mathrm{.}0050m^3($State $1).$ The cylinder is then slowly cooled with a heat transfer

of $1\mathrm{.}95$ kJ from the cylinder to the surroundings until the gas volume

decreases to $0\mathrm{.}0025m^3($State $2).$

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