# Reversed Carnot Cycle

Unlike the Carnot heat engine, the Carnot refrigeration cycle undergoes a process with opposite direction. We see from the model, heat QL is absorbed from the low-temperature reservoir (TL=constant) and heat QH is rejected to a high-temperature reservoir (TH=constant). In this case a work input in the amount of Wrev is required to achieve this process. And we know from the 1st law of thermodynamics, the required work can be determined in  Wrev=- QH – QL. Here QH<0 and QL>0. The reversed Carnot cycle also consists of two isentropic and two isothermal processes. The process undergoes in direction 3-2-1-4-3 This process is isentropic. The engine is perfect insulated so that no heat is lost and absorbed. Gas is compressed slowly until the temperature rises from TL to TH.

Process 2-1: Reversible Isothermal Compression (TH=constant)

During this process, heat is rejected. Gas is compressed reversibly at the constant temperature TH.

This process is isentropic. The engine is perfect insulated so that no heat is lost and absorbed. Gas expands slowly until the temperature drops from TH to TL.

Process 4-3: Reversible Isothermal Expansion (TL=constant)

During this process, heat is absorbed. Gas is compressed reversibly at the constant temperature TH.

The coefficient of performance (COP) of any refrigerator or heat pump, reversible or irreversible, can be calculated with the general expression:

• For a Carnot refrigerator: • For a Carnot heat pump: From the T-s-diagram, we obtain: Qab=QH = TH∙ ΔS2→1

Qzu=QL = TL∙ ΔS4→3

ΔS2→1= – ΔS4→3

Therefore

• For a Carnot refrigerator: • For a Carnot heat pump: According to coefficient of performance (COP), we can also draw the following conclusions:

1. The coefficient of performance (COP) of a reversed Carnot cycle only depends on the highest and lowest temperature.
2. Normally TH>TL, so that means COPR>1 and COPHP>1
3. Both coefficients of performance (COP) have a relationship: COPHP = COPR +1
4. If TL decreases, both COPR and COPHP decrease.

As mentioned above, the reversed Carnot cycle is a reversible process. Hence, if a real refrigerator has the coefficient of performance of COP, then:

• COPR < COPR,rev: irreversible refrigerator
• COPR = COPR,rev: reversible refrigerator
• COPR > COPR,rev: unrealistic refrigerator