krypton, a noble gas $($Cv $=0\mathrm{.}14883,$ Cp $=0\mathrm{.}24805,$ R $=0\mathrm{.}09921,$ all in kJ$/$kg$*$K$),$ is contained in a frictionless piston cylinder device. the gas is initially at $456$ kPa and $55$ deg C$.$ the gas is expanded such that PV$1\mathrm{.}246$ is constant, until the final temperature is $22$ deg C$.$ determine the amount $($kJ$/$kg$)$ and the direction $($IN$/$OUT$)$ of the heat transfer for the gas necessary to accomplish this process