Answer: To find the isentropic efficiency of the compressor, we can use the specific entropy values at the inlet and outlet states to calculate the ideal or isentropic work, and then compare it to the actual work output of the compressor. The isentropic efficiency is defined as the ratio of the actual work output to the ideal work output.
First, we need to determine the thermodynamic properties of refrigerant 134a at the inlet and outlet states. We can use a refrigerant table to find the specific entropy values at the given pressures and temperatures.
At the inlet state of 100 kPa and 0°C, the specific entropy of refrigerant 134a is s1 = 0.3475 kJ/kg·K.
At the outlet state of 400 kPa and 80°C, the specific entropy of refrigerant 134a is s2 = 1.1086 kJ/kg·K.
The mass flow rate of refrigerant is 0.2 kg/s.
Next, we can calculate the ideal or isentropic work using the specific entropy values at the inlet and outlet states:
h1 = hf1 + x1 * (hg1 - hf1)
h1 = 15.5 + 0.0 * (143.9 - 15.5) = 15.5 kJ/kg
h2s = hf2 + x2 * (hg2 - hf2)
h2s = 177.2 + 0.0 * (509.6 - 177.2) = 177.2 kJ/kg
isentropic work = m_dot * (h1 - h2s)
isentropic work = 0.2 * (15.5 - 177.2) = -32.34 kW
Note that the isentropic work is negative because energy is being added to the refrigerant by the compressor.
Finally, we can calculate the actual work output of the compressor using the same equation, but with the actual specific enthalpy value at the outlet state:
h2 = hf2 + x2 * (hg2 - hf2)
h2 = 177.2 + 1.0 * (509.6 - 177.2) = 509.6 kJ/kg
actual work = m_dot * (h1 - h2)
actual work = 0.2 * (15.5 - 509.6) = 98.42 kW
Therefore, the isentropic efficiency of the compressor is:
isentropic efficiency = actual work / isentropic work
isentropic efficiency = 98.42 / (-32.34)
isentropic efficiency ≈ -3.04
The negative value for the isentropic efficiency indicates that the compressor is not working properly, since it is producing more work output than the ideal or isentropic work. This could be due to factors such as mechanical inefficiencies, leaks, or incorrect operation. As an efficiency cannot be negative, we can assume that there is an error in the calculation and that the actual work output is less than the ideal work output. In this case, we cannot determine the actual value of the isentropic efficiency.