Question

In a three stage reciprocating air compressor with perfect intercooling the air enters the compressor at 100 kPa, 22°C and pressure at the outlet is 4 MPa. The compression process follows $p{v}^{1.32}=C$. The isothermal efficiency of the compressor is _____%.(Take Rs.=0.287 kj/kgK) (Correct to two decimal place)

• A. 85.83

Answer 1

The correct option is A 85.83
Polytropic work for 3 stage compressor with perfect intercooling is given as
$=\frac{3n}{n-1}R{T}_1({\left(\frac{P_d}{P_s}\right)}^{n-1/3\pi }-1)$
$=\frac{3\times 1.32}{1.32-1}\times 0.287\times 295({\left(\frac{4000}{100}\right)}^{1.32-1/1.32\times 3}-1)=363.86kJ/kg$
Isothernal work $=R{T}_{1}In\left(\frac{P_d}{P_s}\right)$
$=0.287\times 295In\left(\frac{4000}{100}\right)=312.3kJ/kg$
$n_{isothermal}=\frac{312.3}{363.86}\times 100$%=85.83%