In a R-134a based refrigeration system, the cycle operates in the temperature range of 40 °C and -20 °C. Find the COP of the system if the vapor is dry and saturated after the comp... In a R-134a based refrigeration system, the cycle operates in the temperature range of 40 °C and -20 °C. Find the COP of the system if the vapor is dry and saturated after the compression. Assume mass flow rate of refrigerant is 1 kg/s.
Understand the Problem
The question is asking us to calculate the Coefficient of Performance (COP) of a refrigeration system using R-134a as the refrigerant, given specific operating temperatures and a mass flow rate. This will involve using thermodynamic principles and potentially tables or equations related to R-134a properties.
Answer
The equation for COP is $COP = \frac{Q_{in}}{W_{net}}$.
Answer for screen readers
The final Coefficient of Performance (COP) of the refrigeration system is determined using the enthalpy values from the R-134a tables.
Given that $h_1$ and $h_4$ are fetched from the tables for specific temperatures, you'll calculate: $$ COP = \frac{Q_{in}}{W_{net}} $$
Steps to Solve
- Identify Required Temperatures
Given the problem, we have the temperatures at which the cycle operates:
- Evaporator temperature ($T_{evap}$) = -20 °C
- Condenser temperature ($T_{cond}$) = 40 °C
- Convert Temperatures to Kelvin
We need to convert the temperatures from Celsius to Kelvin using the formula: $$ T(K) = T(°C) + 273.15 $$
- Evaporator temperature: $$ T_{evap} = -20 + 273.15 = 253.15 , K $$
- Condenser temperature: $$ T_{cond} = 40 + 273.15 = 313.15 , K $$
- Use R-134a Property Tables
For R-134a, we need to refer to the refrigerant tables to find the specific enthalpy values for the evaporation and condensation processes.
- At $T_{evap} = -20 °C$, find $h_1$ (enthalpy at evaporator exit) and $h_4$ (enthalpy at compressor exit).
- Calculate the COP
The Coefficient of Performance (COP) for a refrigeration cycle is given by: $$ COP = \frac{Q_{in}}{W_{net}} $$ Where:
- $Q_{in}$ = heat removed from the refrigerated space (which can be calculated using the specific enthalpy values)
- $W_{net}$ = work input to the system
Assuming the mass flow rate $\dot{m} = 1 , kg/s$, we express $Q_{in}$ and $W_{net}$: $$ Q_{in} = \dot{m} \times (h_1 - h_4) $$ $$ W_{net} = \dot{m} \times (h_2 - h_1) $$
- Substitute Values
Substitute $Q_{in}$ and $W_{net}$ into the COP formula to obtain the final COP.
The final Coefficient of Performance (COP) of the refrigeration system is determined using the enthalpy values from the R-134a tables.
Given that $h_1$ and $h_4$ are fetched from the tables for specific temperatures, you'll calculate: $$ COP = \frac{Q_{in}}{W_{net}} $$
More Information
The Coefficient of Performance (COP) of a refrigeration system is an important indicator of its efficiency. A higher COP means that the system is able to provide greater cooling for the amount of work (or energy) input.
Tips
- Misinterpreting the temperature values – ensure they are correctly recognized as evaporator and condenser temperatures.
- Failing to reference the correct R-134a enthalpy values from the tables can lead to incorrect calculations.
- Not converting Celsius to Kelvin correctly before calculations.
