A

Step 1: The equation given is \( pV^n = p_0 V_0^n \).
Here, we have one mole of an ideal gas, thus we can apply the ideal gas law \( PV = nRT \), where \( n = 1 \) mole, and is thus \( P = \frac{RT}{V} \).
Step 2: Since we're looking for temperature when \( V = V_0 \), we can substitute into the ideal gas law: \( P_0 = \frac{RT_0}{V_0} \) for initial conditions.
Also, we can calculate \( P \): substituting this into the equation gives us \( P_0 V_0^n = \frac{RT_0}{V_0} V_0^n \) when \( V = V_0 \).
Step 3: Rearranging gives \( T_0 = \frac{P_0 V_0^n}{R} V_0^{1-n} \). From the original equation, we know \( n = 1 \), so \( T_0 = \frac{P_0 V_0}{R} \).
Therefore, the temperature of the gas when \( V = V_0 \) is given by \( T_0 = \frac{P_0 V_0}{R} \), which corresponds to option A.