Answer
$\frac{Q}{p_1V_1} = 4.5$
Work Step by Step
Step 2 : Pressure increase from $p_1$ to $2.00p_1$
The work done is given by
$W = nC_v\Delta T$
Where $C_v = \frac{3}{2} R$
$W = n \frac{3}{2} R\Delta T$
$W = n \frac{3}{2} R(T_2 - T_1)$
$W = \frac{3}{2} nR T_1 (\frac{T_2}{T_1} - 1)$
$W = \frac{3}{2} p_1V_1(4 - 1)$
$W = \frac{9}{2} p_1V_1$
$\frac{Q}{p_1V_1} = \frac{9}{2}$
$\frac{Q}{p_1V_1} = 4.5$
