Answer to Question #215328 in Molecular Physics | Thermodynamics for Wavie

Question

In a single-acting two-stage reciprocating air compressor 4.5 kg of air per min are compressed from 1.013 bar and 15°C through a pressure ratio of 9 to 1. Both stages have the same pressure ratio, and the law of compression and expansion in both stages ispv^1.3=c . If intercooling is complete, calculate the indicated power and the cylinder swept volume required. Assume that the clearance volumes of both stages are 5% of their respective swept volumes and that the compressor runs at 300 rev/min.

Answer 1

$W=\frac{2n}{n-1}p_1V_1((\frac{p_d}{p_s})^{\frac{n-1}{2n}}-1)=\frac{2n}{n-1}mRT_1((\frac{p_d}{p_s})^{\frac{n-1}{2n}}-1)=$

$\frac{2\cdot 1.3}{1.3-1}\cdot 2 .57\cdot 287\cdot298((\frac{9}{1})^{\frac{1.3-1}{2\cdot 1.3}}-1)=1.12\frac{MNm}{min}.$