Question

Which of the following relation represents the minimum work input required in a multi-stage reciprocating compressor with perfect intercooling?
Where N is the number of stages and n is the polytropic index of compression

• A. $N\left(\frac{n}{n-1}\right)P_1{V}_1[{\left(\frac{P_2}{P_1}\right)}^{N\left(\frac{N-1}{5}\right)}-1]$
• B. $N\left(\frac{n}{n-1}\right)P_1{V}_1[{\left(\frac{P_2}{P_1}\right)}^{\frac{n-1}{n}}-1]$
• C. $N\left(\frac{n}{n-1}\right)P_1{V}_1[{\left(\frac{P_2}{P_1}\right)}^{\frac{n-1}{Nn}}-1]$
• D. $\left(\frac{n-1}{n}\right)P_1{V}_1[{\left(\frac{P_2}{P_1}\right)}^{\frac{Nn}{n-1}}-1]$

Answer 1

The correct option is C $N\left(\frac{n}{n-1}\right)P_1{V}_1[{\left(\frac{P_2}{P_1}\right)}^{\frac{n-1}{Nn}}-1]$

$N\left(\frac{n}{n-1}\right)P_1{V}_1[{\left(\frac{P_2}{P_1}\right)}^{\frac{n-1}{Nn}}-1]$