Question

In a three - stage air compressor with perfect intercooling, air enters at 96 kPa and 25${}^{\circ }$C and delivers at 3 MPa. If the compressor process is polytropic $(p{V}^{1.3}=C)$, the isothermal efficiency of the compressor is

• A. 87.34 %
• B. 85.2 %
• C. 90.28 %
• D. 86.95 %

Answer 1

The correct option is A 87.34 %

$p_1=96kPa$

$T_1=25+273=298K$

$p_4=3MPa$

Polytropic index,n = 1.3



${\text{compressor work,W}}_{poly}=N\left(\frac{n}{n-1}\right)R{T}_1[{\left(\frac{p_4}{p_1}\right)}^{(n-1/nN)}-1]$

$=3\left(\frac{1.3}{1.3-1}\right)\times 0.287\times 298[{\left(\frac{3000}{96}\right)}^{(1.3-1)/1.3\times 3}-1]$

$W_{poly}=337.0338kJ/kg$

${\text{Isothermal work,W}}_{iso}=R{T}_{1}ln\left(\frac{p_4}{p_1}\right)$

$W_{iso}=0.287\times 298ln\left(\frac{3000}{96}\right)=294.382kJ/kg$

$\text{Isothermal efficiency,}{\eta }_{iso}=\frac{W_{iso}}{W_{poly}}=\frac{294.382}{337.0338}=87.34\%$