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2 months ago

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Helium gas is compressed from 90 kPa and 30oC to 450 kPa in a reversible, adiabatic process. Determine the final temperature and

the work done, assuming the process takes place (a) in a piston-cylinder device and (b) in a steadyflow compressor. [15

1 answer:

choli [298]2 months ago

4 0

Answer:

T2 ( final temperature ) = 576.9 K

a) 853.4 kJ/kg

b) 1422.3 kJ / kg

Explanation:

given data:

pressure ( P1 ) = 90 kPa

Temperature ( T1 ) = 30°c + 273 = 303 k

P2 = 450 kPa

To determine final temperature in an Isentropic process

$T2 = T1 (\frac{p2}{p1} )^{(k-1)/k}$ ----------- ( 1 )

T2 = 303 $( \frac{450}{90})^{(1.667- 1)/1.667}$ = 576.9K

The work performed in a piston-cylinder device is calculated using the subsequent formula

$w_{in} = c_{v} ( T2 - T1 )$ ------- ( 2 )

where: cv = 3.1156 kJ/kg.k for helium gas

T2 = 576.9K, T1 = 303 K

substituting values into equation 2

$w_{in}$ = 853.4 kJ/kg

the work done in a steady flow compressor is determined using this

$w_{in} = c_{p} ( T2 - T1 )$

where: cp ( constant pressure of helium gas ) = 5.1926 kJ/kg.K

T2 = 576.9 k, T1 = 303 K

plugging values back into equation 3

$w_{in}$ = 1422.3 kJ / kg

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