Question

Refrigerant-134a enters an adiabatic compressor as saturated vapor at \(-24^{\circ} \mathrm{C}\) and leaves at \(0.8 \mathrm{MPa}\) and \(60^{\circ} \mathrm{C}\) The mass flow rate of the refrigerant is \(1.2 \mathrm{kg} / \mathrm{s}\). Determine (a) the power input to the compressor and ( \(b\) ) the volume flow rate of the refrigerant at the compressor inlet.

Short answer

Question: Determine the power input to the adiabatic compressor and the volume flow rate at the inlet for a refrigerant with a mass flow rate of 0.4 kg/s, entering at a temperature of -24°C and pressure p1 as saturated vapor, and leaving at 60°C and 0.8 MPa. Assume 100% efficiency for the compressor.

Step-by-step solution

Get the specific volume and specific enthalpy of the refrigerant at both inlet and outlet

Look up the thermodynamic properties of Refrigerant-134a in the property tables for the given inlet and outlet conditions. We are looking for the specific volume v1 and specific enthalpy h1 at -24°C and saturated vapor condition, and v2 and h2 at 60°C and 0.8 MPa.

Calculate the work done on the refrigerant by the compressor (isentropic work)

To find the work done on the refrigerant, first, we assume an isentropic process. Then, the isentropic work can be determined using the specific enthalpy difference and mass flow rate. Isentropic work, \(W_s = m \cdot (h_2 - h_1)\) where m is the mass flow rate, h1 is the specific enthalpy at the inlet, and h2 is the specific enthalpy at the outlet.

Calculate the power input to the compressor

To find the power input, we must account for the adiabatic efficiency of the compressor. Let's denote it by η. For an adiabatic compressor, the actual work is given by the following equation: \(W_{actual} = \dfrac{W_s}{η}\) Since we are not given the efficiency, we can assume the compressor is 100% efficient (ideal case). In that case, the actual power input would simply be equal to the isentropic work: \(W_{actual} = W_s\) Calculate the power input to the compressor using the specific enthalpy values from Step 1 and the given mass flow rate.

Calculate the volume flow rate at the compressor inlet

The volume flow rate at the inlet can be calculated as the product of the mass flow rate and the specific volume at the inlet: Volume flow rate, \(Q_{inlet} = m \cdot v_1\) Calculate the value of the volume flow rate using the mass flow rate and specific volume obtained in Step 1. Now, you should have the values for (a) the power input to the compressor and (b) the volume flow rate of the refrigerant at the compressor inlet.