For a two-stage reciprocating compressor, compression from pressure \[{{p}_{1}}\] to \[{{p}_{3}}\] is with perfect intercooling and no pressure losses. If compression in both cylinders follows the same polytropic process and the atmospheric pressure is \[{{p}_{a'}}\] then the intermediate pressure \[{{p}_{2}}\] is given by:

• A. \[{{p}_{2}}=({{p}_{1}}+{{p}_{3}})/2\]
• B. \[{{p}_{2}}=\sqrt{{{p}_{1}}.{{p}_{3}}}\]
• C. \[{{p}_{2}}={{p}_{a}}\frac{{{p}_{3}}}{{{p}_{1}}}\]
• D. \[{{p}_{2}}={{p}_{a}}.\sqrt{{{{p}_{3}}}/{{{p}_{1}}}\;}\]