A pistoncylinder device initially contains $0\mathrm{.}5$ m$3$ of nitrogen gas at $400$ kPa and $27$C$.$ An electric heater within the device is turned on and is allowed to pass a current of $2$ A for $6$ min from a $120-$V source. Nitrogen expands at constant temperature to double the initial volume, and a heat loss of $3024$ J occurs during the process. Determine the change of internal energy of nitrogen in kJ$/$kg$.$