Air enters a compressor at atmospheric temperature and pressure of 1 bar and 30°C. It leaves the compressor at 4.9 bar, 181°C and 90 m/s. The isothermal efficiency of compressor is____ %. (Neglect inlet velocity and potential energy.) (Take $c_{p}$ = 1.005 kJ/kgK, R=0.287 kJ/kgK)

91.3

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Solution

The correct option is A 91.3
Given,

$P_{1}$ = 1 bar,
$T_{1}$ = 30 + 273 = 303 K

$P_{2}$ = 4.9 bar,
$T_{2}$ = 181 + 273 = 454 K

$V_{2}$ = 90 m/s,
$V_{1}$ = 0 m/s,

$c_{p}$ = 1.005 kJ/kgK,
R = 0.287 kJ/kgK

Actual work of compression

$W_{a} = (h_{1} - h_{2}) - (\frac{V_{2}^{2}}{2})$ [By SFEE]

$= c_{p} (T_{1} - T_{2}) - \frac{90^{2}}{2 \times 1000}$

$= 1.005 \times (303 - 454) - \frac{8100}{2000}$

$= - 155.805 k J / k g$

Isothermal work of compression,

$W_{T} = \int_{1}^{2} v d p - \frac{V_{2}^{2}}{2000} = - R T_{1} l n \frac{V_{2}^{2}}{2000}$

$= - 0.287 \times 303 l n (4.9) - \frac{90^{2}}{2000}$

$= - 138.201 - 4.05$

$W_{T} = - 142.251 k J / k g$

isothermmal efficiency

$η_{T} = \frac{W_{T}}{W_{n}} = \frac{- 142.251}{- 155.805} = 0.913 = 91.3$

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