One mole of an ideal gas at 900 K, undergoes two reversible processes, I followed by II, as shown below. If the work done by the gas in the two processes are the same, the value of \(\ln \frac{v_3}{v_2}\) is _____

(U: internal energy, S: entropy, p: pressure, V: volume, R: gas constant)
(Given: molar heat capacity at constant volume, \(C_v,m\) of the gas is \(\frac{5}{2}\)R)