Helium $($He$)$ gas initially at $p1,T1$ undergoes a polytropic process, with $n=k,$ to a final pressure of p $2.$ Determine the work and heat transfer per unit mass for the process. Assume ideal gas behavior and use constant specific heat. Use $c_p=2R.$ Express the answer with given parameters such as p$1,$ p$2,$ T$1,$ k$,$ and R$.$