Vapour Compression Cycle

The Minimum Amount of Work to Drive a Heat Pump is defined in terms of the Absolute Temperature Scale

Here we show again the diagram that was used to help explain the Reversible Carnot Cycle. It shows a reversible engine E driving a reversible heat pump P. The relationship between Q1, Q2 and W depends only on the temperatures of the hot and cold reservoirs, just as Carnot predicted. But temperature must be defined in a more fundamental way. The degrees on the thermometer are only an arbitrary scale. Kelvin took the bold step in 1851 of defining an absolute temperature scale in terms of the efficiency of reversible engines:

The ideal "never attainable" efficiency is the ratio of work output to heat input (W/Q1) of the reversible engine E and it equals: Temperature Difference (T1 - T0) divided by the Hot Reservoir Temperature (T1). It is known as the Carnot efficiency, taking its name from Sadi Carnot.

The device P can be any refrigeration device we care to invent, and the work of Kelvin tells us that the Minimum Work, W necessary to lift a quantity of heat Q2 from temperature T0 to temperature T1 is:

Q2 multiplied by the ratio Temperature Difference (T1 - T0)/Cold Reservoir Temperature (T0). The temperatures must be measured on an Absolute scale.

Choose a fluid, or refrigerant, which vaporizes at a lower temperature than the space to be cooled. Heat then flows from the cool space (downhill) and vaporizes the refrigerant. This is represented by the section 1 - 2 of the orange line. Then, instead of just letting it boil away and disappear as vapour, it is captured, and pressurized (2 - 3). At the high pressure its boiling point, or evaporating temperature is much higher. So it can condense at this higher temperature, giving up its latent heat which flows (downhill again) to the warm air outside (3 - 4). When it has become a liquid, the pressure is reduced (4 - 1) and the process can start again.

This is the most widely used process for providing cooling. It is called the Vapour Compression Cycle, and it finds application on equipment ranging from domestic refrigerators and freezers to large cold stores and building air conditioning systems.

Pressure - Enthalpy

In order to study this process more closely, refrigeration engineers use this pressure - enthalpy diagram. "P" is the symbol for Pressure, and "h" is the symbol for Enthalpy. This diagram is a way of describing the liquid and gas phase of a substance. On the vertical axis is pressure, and on the horizontal, enthalpy. Enthalpy can be thought of as the quantity of heat in a given quantity, or mass of substance. The curved line is called the saturation curve and it defines the boundary of pure liquid and pure gas, or vapour. In the region marked vapour, its pure vapour. In the region marked liquid, its pure liquid. If the pressure rises so that we are considering a region above the top of the curve, there is no distinction between liquid and vapour. Above this pressure the gas cannot be liquified. This is called the Critical Pressure. In the region underneath the curve, there is a mixture of liquid and vapour.