Question

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

Answer 1

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

Determine final temperature for an Isentropic  process

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

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

Work done in a piston-cylinder device can be calculated using this formula

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

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

             T2 = 576.9K ,    T1 = 303 K

substitute given values Back to equation 2

$w_{in}$  = 853.4 kJ/kg

work done in a steady flow compressor can be calculated 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

substitute values back to equation 3

$w_{in}$ = 1422.3 kJ / kg