For maximum work output in a two stage expansion gas turbine with perfect, the intermediate pressure (P) has the following relationship with maximum pressure ($$P_1$$) and minimum pressure ($$P_2$$) of the cycle:

A

$$P = \sqrt{\frac{P_1 + P_2}{P_1 - P_2}}$$

B

$$P = \sqrt{P_1P_2}$$

C

$$P = \left(\frac{P_1}{P_2}\right)^{\frac{1}{2}}$$

D

$$P = \left(\frac{P_1 + P_2}{4}\right)^{\frac{1}{2}}$$