Answer
$\frac{W}{p_1V_1} = 3.00$
Work Step by Step
We know that,
initial volume : $V_i = \frac{V_1}{2}$
Final volume : $V_f = 2V_1$
Pressure, $p' = 2.00p_1$
the first law of thermodynamics is
$Q = 0 + W$
$W = p'\Delta V$
$W = p' (V_f - V_i)$
$W = 2.00p_1(2.00V_1 - \frac{V_1}{2})$
$W = 4.00 p_1V_1 - p_1V_1$
$W = 3.00 p_1V_1$, so
$\frac{W}{p_1V_1} = 3.00$
