For a two stage reciprocating compressor, compression from p₁ to p₃ is with perfect intercooling and no pressure losses. If compression in both the cylinders follows the same polytropic process and the atmospheric pressure is p_a, then the intermediate pressure p₂ is given by

A. $${{\text{p}}_2} = \frac{{{{\text{p}}_1} + {{\text{p}}_3}}}{2}$$

B. $${{\text{p}}_2} = \sqrt {{{\text{p}}_1}{{\text{p}}_3}} $$

C. $${{\text{p}}_2} = {{\text{p}}_{\text{a}}} \times \frac{{{{\text{p}}_3}}}{{{{\text{p}}_1}}}$$

D. $${{\text{p}}_2} = {{\text{p}}_{\text{a}}}\sqrt {\frac{{{{\text{p}}_3}}}{{{{\text{p}}_1}}}} $$

Answer: Option B