Air undergoes a polytropic compression in a piston cylinder assembly from $P_1=1$ $atm$ and $20^{\circ}$$C$ to $P_2 = 5$ $atm$. Using ideal gas model, find the work and the heat transfer per unit mass if $n=1.3$.

A. $w= -126$ $kJ/kg$ ; $Q/m=-31.3$ $kJ/kg$
B. $w= 126$ $kJ/kg$ ; $Q/m=31.3$ $kJ/kg$
C. $w= 63$ $kJ/kg$ ; $Q/m=15.5$ $kJ/kg$
D. $w= -63$ $kJ/kg$ ; $Q/m=-15.5$ $kJ/kg$