Question

Consider an ideal gas refrigeration cycle using helium as the working fluid. Helium enters the compressor at 120 kPa and 21°C and compressed to 440 kPa. Helium is then cooled to 16°C before it enters the turbine. Assume constant heat capacity of helium. For a mass flow rate of 0.24 kg/s, the net power input required is:

Answer 1

Answer:
`W_(net)=103.72 kJ/s`

Step-by-step explanation:

Given

`P_1=120kPa`

`T_1=21^(\circ)C\approx 294K`

`P_2=440kPa`

`T_3=16^(\circ)C\approx 289 K`

`T_2` is the compressor exit temperature and is given by

`\gamma` for helium is
`(5)/(3)`

`C_p` for helium is
`5.1926 kJ/kg-K`

`T_2=T_1\left [ (440)/(120)\right ]^(\gamma -1)/(\gamma )`

`T_2=494.37 K`

Now Turbine Exit Pressure is given By

`T_4=T_3\left [ (120)/(440)\right ]^(\gamma -1)/(\gamma )`

`T_4=289\left [ (120)/(440)\right ]^((5)/(3) -1)/((5)/(3))`

`T_4=171.865 K`

`W_(net)=mC\left ( \left ( T_2-T_1\right )-\left ( T_3-T_4\right )\right )`

`W_(net)=0.24* 5.1926\left ( \left ( 494.37-294\right )-\left ( 289-171.865\right )\right )`

`W_(net)=0.24* 5.1926* 83.235`

`W_(net)=103.72 kJ/s`