Question

Refrigerant 134a enters an insulated compressor operating at steady state as saturated vapor at -12oC with a volumetric flow rate of 0.18 m3/s. Refrigerant exits at 7 bar, 70oC. Changes in kinetic and potential energy from inlet to exit can be ignored. Determine the volumetric flow rate at the exit, in m3/s, and the compressor power, in kW.

Answer 1

Answer:

$\dot V_{out} = 0.061\,\frac{m^{3}}{s}$, $\dot W = 108.875\,kW$

Explanation:

The process in the compressor is modelled after the First Law of Thermodynamics:

$\dot W + \dot m \cdot (h_{1}-h_{2}) = 0$

The specific enthalpies of the refrigerant at inlet and outlet are, respectively:

Inlet (Saturated vapor)

$\nu = 0.10744\,\frac{m^{3}}{kg}$

$h = 243.34\,\frac{kJ}{kg}$

Outlet (Superheated Vapor)

$\nu = 0.036373\,\frac{m^{3}}{kg}$

$h = 308.34\,\frac{kJ}{kg}$

The mass flow is:

$\dot m = \frac{\left(0.18\,\frac{m^{3}}{s} \right)}{0.10744\,\frac{m^{3}}{kg} } \co$

$\dot m = 1.675\,\frac{kg}{s}$

The volumetric flow rate at the exit is:

$\dot V_{out} = \left(1.675\,\frac{kg}{s} \right)\cdot \left(0.036373\,\frac{m^{3}}{kg} \right)$

$\dot V_{out} = 0.061\,\frac{m^{3}}{s}$

The power needed to make the compressor work is:

$\dot W = \dot m \cdot (h_{2}-h_{1})$

$\dot W = \left(1.675\,\frac{kg}{s} \right)\cdot \left(308.34\,\frac{kJ}{kg}-243.34\,\frac{kJ}{kg} \right)$

$\dot W = 108.875\,kW$