Thermodynamics eBook: Carnot Refrigerator and Heat Pump

Ch 5. Second Law of Thermodynamics					Multimedia Engineering Thermodynamics
Heat Engine	The Second Law	Carnot Cycle	Carnot Heat Engine	Carnot Refrigerator

THERMODYNAMICS - THEORY

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 Q_L is received by the gas from a heat sink and heat in the amount of Q_H is rejected to a heat source, and a work input of W_net,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

COP_R = 1/((Q_H/Q_L)-1)

COP_HP = 1/(1-(Q_L/Q_H))

where
      Q_H = the amount of heat rejected to the
             high-temperature reservoir
      Q_L = 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,

COP_R,rev = 1/((T_H/T_L)-1)

COP_HP,rev = 1/(1-(T_L/T_H))

where
      T_H = the absolute temperature of the
             high-temperature reservoir
      T_L = the absolute temperature of the
             low-temperature reservoir

The Carnot Heat Pump Has the
Highest COP

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

COP_R	< h_R,rev	irreversible refrigerator
	= h_R,rev	reversible refrigerator
	> h_R,rev	impossible refrigerator

COP_HP	< h_HP,rev	irreversible heat pump
	= h_HP,rev	reversible heat pump
	> h_HP,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.