Question

Refrigerant 134a enters an insulated compressor operating at steady state as saturated vapor at 2208C with a mass flow rate of 1.2 kg/s. Refrigerant exits at 7 bar, 708C. Changes in kinetic and potential energy from inlet to exit can be ignored. Determine (a) the volumetric flow rates at the inlet and exit, each in m3 /s, and (b) the power input to the compressor, in kW.'

Answer 1

a)
`V_1=4.88m^2/s`

`V_2=4.88m^2/s`

b)
`P=-119.18kW`

Step-by-step explanation:

From the question we are told that:

Steady State Saturated vapor
`T_1= -20C=>253k`

Mass Flow rate
`M=1.2kg/s`

Exit Pressure
`P_2=7bar`

Exit Temperature
`T_2=70C=>373k`

From Refrigerant 134a Properties

`T_1= -20C =>P_1=1.399 bar`

Generally the equation for Volumetric Flow rate is mathematically given by

For Inlet

`V_1=m(RT_1)/(P_1)`

`V_1=m(8314*253)/(1.399*10^3)`

`V_1=18.97m^2/s`

For outlet

`V_2=m(RT_2)/(P_2)`

`V_2=1.2*(8314*343)/(7*10^3)`

`V_2=4.88m^2/s`

b)

Generally the equation for Steady state mass and energy equation is mathematically given by

`P=m(h_1-h_2)`

From Refrigerant 134a Properties

`T_1= -20C =>h_1=24.76kJ/kg`

`T_2= 70C =>h_2=124.08kJ/kg`

Therefore

`P=1.2(12.76-124.08)`

`P=-119.18kW`

Therefore

Power input into the compressor is

`P=-119.18kW`