Answer
$\frac{Q}{p_1V_1} = 0.693$
Work Step by Step
Step 1 : Isothermal expansion to volume $2.00V_1$
To find the $\frac{Q}{p_1V_1}$, the first law of thermodynamics is
$Q = 0 + W$
$Q = nRT_1 ln \frac{V_2}{V_1}$
$Q = nRT_1 ln \frac{2.00 V_1}{V_1}$
$Q = p_1V_1 ln 2$
$\frac{Q}{p_1V_1} = ln 2$
$\frac{Q}{p_1V_1} = 0.693$
