For minimum compression work in a 2 - stage reciprocating air compressor, which of the following expressions gives the ratio of low pressure cylinder to high pressure cylinder diameters?

Where P1 P2 and P3 are suction, intermediate and delivery pressures respectively.

1
\({\left( {\frac{{{P_3}}}{{{P_1}}}} \right)^{\frac{1}{4}}}\)
2
\({\left( {\frac{{{P_3}}}{{{P_1}}}} \right)^{\frac{1}{3}}}\)
3
\({\left( {\frac{{{P_3}}}{{{P_1}}}} \right)^{\frac{1}{2}}}\)
4
\({\left( {\frac{{{P_3}}}{{{P_2}}}} \right)^{\frac{1}{4}}}\)

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