Question

How does the COP of a cascade refrigeration system compare to the COP of a simple vapor-compression cycle operating between the same pressure limits?

Short answer

Question: Compare the Coefficient of Performance (COP) of a cascade refrigeration system to the COP of a simple vapor-compression cycle operating between the same pressure limits. Answer: The cascade refrigeration system generally has a higher Coefficient of Performance (COP) compared to the simple vapor-compression cycle when operating between the same pressure limits. The higher COP in the cascade system is due to its ability to maintain low compressor pressure ratios by dividing the total pressure difference between two or more simple vapor-compression cycles, which reduces irreversibilities in each cycle and results in less work input.

Step-by-step solution

Understand Coefficient of Performance (COP)

The Coefficient of Performance (COP) is the ratio of the useful cooling effect (also known as refrigeration effect) to the amount of work input in a refrigeration cycle. It is an essential parameter to measure the efficiency of a refrigeration system. Mathematically, the COP is given by: COP = \( \frac{Q_{L}}{W} \) where \(Q_{L}\) is the amount of heat absorbed at the lower temperature (refrigeration effect) and W is the work input to the cycle.

Simple vapor-compression cycle COP

The simple vapor-compression cycle consists of four processes: evaporation, compression, condensation, and expansion. The COP for a simple vapor-compression cycle can be expressed as: \(COP_{vc} = \frac{Q_{L}}{W_{vc}}\) where \(W_{vc}\) is the work input to the simple vapor-compression cycle.

Cascade refrigeration cycle COP

In a cascade refrigeration system, two or more simple vapor-compression cycles are connected in series, working between different temperature levels. As such, the COP for a cascade refrigeration cycle can be expressed as: \(COP_{cascade} = \frac{Q_{L}}{W_{cascade}}\) where \(W_{cascade}\) is the work input to the cascade refrigeration cycle.

Comparing COPs of the two systems

Let both systems operate between the same pressure limits; we want to compare their COPs to determine which system yields a better performance. We have: \(COP_{vc} = \frac{Q_{L}}{W_{vc}}\) \(COP_{cascade} = \frac{Q_{L}}{W_{cascade}}\) Generally, cascade refrigeration systems have a higher COP than simple vapor-compression systems when operating between the same pressure limits. CASCADE system's high COP is attributed to its ability to maintain low compressor pressure ratios by dividing the total pressure difference between two or more simple vapor-compression cycles, which reduces the irreversibilities in each cycle and results in less work input. To demonstrate this comparison, we can say that: \(COP_{cascade} > COP_{vc}\) This tells us that the cascade refrigeration system has a higher Coefficient of Performance than the simple vapor-compression cycle when both systems are operating between the same pressure limits.