The Reversed Carnot Cycle

P-v Diagram of the Reversed Carnot Cycle

The Carnot cycle is a totally reversible cycle. The Carnot refrigeration cycle can be achieved if one reverses all the processes in the Carnot power cycle. In this case, heat in the amount of QL is received by the gas from a heat sink and heat in the amount of QH is rejected to a heat source, and a work input of Wnet,in is required to accomplish the cycle. The P-v diagram of the reversed Carnot cycle is shown on the left.

  The Carnot Refrigerator and Heat Pump

A refrigerator or a heat pump that operates on the reversed Carnot cycle is called a Carnot refrigerator or a Carnot heat pump.

The coefficient of performance(COP) of reversible or irreversible refrigerator or heat pump is given by

      COPR = 1/((QH/QL)-1)

      COPHP = 1/(1-(QL/QH))

      QH = the amount of heat rejected to the
             high-temperature reservoir
      QL = the amount of heat received from the
             low-temperature reservoir

For reversible refrigerators or heat pumps, such as Carnot refrigerators, or Carnot heat pumps, the COPs can be determined by replacing the heat transfer ratios in the above equations by the absolute temperature ratios. These are,

      COPR,rev = 1/((TH/TL)-1)

      COPHP,rev = 1/(1-(TL/TH))

      TH = the absolute temperature of the
             high-temperature reservoir
      TL = the absolute temperature of the
             low-temperature reservoir

The Carnot Heat Pump Has the
Highest COP

COPR,rev (or COPHP,rev) is the highest COP a refrigerator (or a heat pump) which operates between a high-temperature reservoir at temperature TH and a low-temperature reservoir at temperature TL can reach. All irreversible refrigerators or heat pumps working between the same two reservoirs have lower COPs.

COPR < hR,rev irreversible refrigerator
= hR,rev reversible refrigerator
> hR,rev impossible refrigerator

COPHP < hHP,rev irreversible heat pump
= hHP,rev reversible heat pump
> hHP,rev impossible heat pump
    Household Refrigerators

How a Refrigerator Works

A Household Refrigerator


The basic idea behind a household refrigerator is simple: it uses the evaporation of the refrigerant to absorb heat from the cooling space in the refrigerator. There are four basic parts to any refrigerator.

  • Compressor
  • Fin coil unit outside the refrigerator
  • Expansion valve
  • Heat-exchanging pipes inside the refrigerator

The basic mechanism of a refrigerator works like this:

  • The compressor compresses the refrigerant vapor, increasing the temperature and pressure of the refrigerant vapor.
  • The high-temperature and high-pressure refrigerant vapor dissipates heat to the ambient when it flow through the fin coil unit outside the refrigerator. The refrigerant vapor condenses into liquid form.
  • The cool liquid refrigerant flows through the expansion valve to reduce its pressure.
  • The cool liquid refrigerant vaporizes when it flows through the fin coil unit inside the refrigerator and receives heat from the inner space of the refrigerator, making the inner space of the refrigerator cold. Then the gas enters the compressor to be compressed again. The cycle repeats itself.

A household refrigerator is a combination of refrigerator-freezer. It is designed to maintain the freezer section at -18 oC and the refrigerator section at 3 oC.