Question

How does the ideal-gas refrigeration cycle differ from the Carnot refrigeration cycle?

Short answer

Question: Briefly explain the differences between the ideal-gas refrigeration cycle and the Carnot refrigeration cycle. Answer: The ideal-gas refrigeration cycle uses a gas as its working fluid and consists of isothermal compression, isobaric heat addition, adiabatic expansion, and isobaric heat rejection. On the other hand, the Carnot refrigeration cycle uses a refrigerant as its working fluid and involves isothermal compression, isothermal heat transfer, isothermal expansion, and isentropic heat rejection. The Carnot cycle is the most efficient but is impractical for most applications due to extreme conditions and high costs, while the ideal-gas cycle is more common in gas turbine and jet engine applications but is less efficient than the Carnot cycle.

Step-by-step solution

Ideal-Gas Refrigeration Cycle

The ideal-gas refrigeration cycle, also known as the reversed Brayton cycle or Joule cycle, is a thermodynamic cycle that uses a gas as the working fluid. It consists of four processes: 1. Isothermal compression - The gas is compressed at a constant temperature. 2. Constant-pressure (isobaric) heat addition - Heat is added to the gas at a constant pressure, causing it to expand and do work on the surroundings. 3. Adiabatic (isentropic) expansion - The gas expands without any heat exchange, causing its internal energy to decrease, and thus its temperature to drop. 4. Constant-pressure (isobaric) heat rejection - Heat is rejected from the gas at a constant pressure, causing it to contract and complete the cycle.

Carnot Refrigeration Cycle

The Carnot refrigeration cycle is a reversible thermodynamic cycle that consists of four processes: 1. Isothermal compression - The refrigerant is compressed at a constant temperature, causing its pressure to increase. 2. Isothermal heat transfer - Heat is added to the refrigerant at a constant temperature, causing it to expand and do work on the surroundings. 3. Isothermal expansion - The refrigerant expands at a constant temperature, causing its pressure to decrease. 4. Adiabatic (isentropic) heat rejection - Heat is rejected from the refrigerant without any change in temperature, causing the refrigerant to contract and complete the cycle.

Key Differences between Ideal-Gas and Carnot Refrigeration Cycles

1. Working fluid: The Ideal-gas refrigeration cycle uses gas as its working fluid, while the Carnot refrigeration cycle uses a refrigerant. 2. Processes: Both cycles involve isothermal compression and isothermal heat transfer. However, the ideal-gas cycle features an adiabatic expansion and isobaric heat rejection, whereas the Carnot cycle features an isothermal expansion and isentropic heat rejection. 3. Efficiency: The Carnot cycle is an ideal cycle and has the highest possible efficiency for a refrigeration cycle operating between two fixed temperatures. However, the ideal-gas refrigeration cycle is not as efficient as the Carnot cycle due to the inefficiencies in the isobaric and adiabatic processes. 4. Practical applications: The Ideal-gas refrigeration cycle is often used in gas turbine and jet engine applications, though it's not widely used in common refrigeration applications. The Carnot cycle, despite being the most efficient cycle, is not practical for most refrigeration applications due to extreme operating conditions and high costs of implementing the isothermal processes. Real-world refrigeration systems often utilize other cycles, such as the vapor-compression or absorption cycles as they are more practical and feasible.