question_answer

If n the polytropic index of compressor and \[\frac{{{p}_{2}}}{{{p}_{1}}}\] is the pressure ratio for a three-stage compressor with ideal intercoolling, the on total work of three stage is:

A) \[\frac{3n}{(n-1)}{{p}_{1}}{{v}_{1}}\,\left\{ {{\left( \frac{{{p}_{2}}}{{{p}_{1}}} \right)}^{(n-1)/n}}-1 \right\}\]

B) \[\frac{n}{(n-1)}{{p}_{1}}{{v}_{1}}\,\left\{ {{\left( \frac{{{p}_{2}}}{{{p}_{1}}} \right)}^{(n-1)/n\,3}}-1 \right\}\]

C) \[\frac{n}{(n-1)}{{p}_{1}}{{v}_{1}}\,\left\{ {{\left( \frac{{{p}_{2}}}{{{p}_{1}}} \right)}^{(n-1)/n}}-1 \right\}\]

D) \[\frac{3n}{(n-1)}{{p}_{1}}{{v}_{1}}\,\left\{ {{\left( \frac{{{p}_{2}}}{{{p}_{1}}} \right)}^{(n-1)/\,3\,n}}-1 \right\}\]