Exploring Richard Mollier's revolutionary impact on refrigeration engineering through practical thermodynamic charts.

Richard Mollier, born in Trieste, Italy, in 1863, was professor of mechanical engineering in Dresden, Germany, from 1897 until his retirement in 1931. He was one of a group of scientists and engineers in Southern Germany in the late 19th century including Clausius, Linde and Zeuner who did much to advance the understanding of the science of refrigeration, but Mollier’s contribution was uniquely practical and is still widely used by designers.

At the beginning of the 20th century, engineers had been building and operating vapor compression refrigeration systems for nearly 50 years but had a very sketchy idea of what was actually happening. Mollier undertook the meticulous task of tabulating the thermal properties of various fluids including ammonia, carbon dioxide, steam and moist air, enabling more accurate computation of system performance, and in 1904 took the radical step of plotting this information in easy-to-use charts. The two most commonly used charts are the temperature-entropy diagram and the pressure-enthalpy chart. The former tends to be favored by academics in thermodynamics because the area under any process traced on the chart is proportional to the work done, whereas the latter form is more useful to practical engineers because the enthalpy difference multiplied by mass flow gives the heat transferred in the evaporator or condenser and the work done in the compressor. To make the scale more useful the pressure is often plotted on a logarithmic axis up the side of the chart, and enthalpy is plotted on a linearscale along the bottom of the chart.

The pressure-enthalpy chart for a refrigerant contains a couple of boundary lines, representing the heat content of the fluid when it is liquid on the point of boiling (the saturated liquid line) and when it is gas on the point of condensing (the saturated vapor line). The horizontal distance between these two lines at any point is the latent heat of the fluid; the amount of energy that needs to be added to turn it from liquid to gas, or conversely the amount of heat to be removed to turn the gas to liquid. The saturated liquid line has a positive gradient on the pressure-enthalpy chart, but the gradient reduces until the line is horizontal. The saturated vapor line at high pressure has a negative gradient and there may be a pressure at which the heat content is maximal; below this pressure the vapor line gradient becomes positive. Thus, the two lines form a dome, meeting at a pressure maximum where their gradients are horizontal.

When working with these charts we routinely talk about points between these two lines as if a homogeneous fluid exists at these points. To fully understand what’s happening inside a refrigeration system, however, it is necessary to appreciate that this is a hypothetical construct; in reality for any point under the dome some of the fluid is liquid and some is gas. From a mathematical point of view this doesn’t matter and the mixture can be treated as a single fluid with enthalpy being the aggregate of the liquid and gas phases. The percentage of gas in the mixture is known as the “quality”—a mixture that is 10% quality means that 90% of the fluid is liquid. This concept is helpful for the math, but it is always important to recognize the practical implications of the two phases when designing systems, especially pipes and heat exchangers. In this sense, high quality means less useful for refrigeration purposes.

Mollier’s charts were of such immense practical value that they quickly became widely used by scientists and engineers around the world as the standard way of calculating system performance. In 1923 at the World Congress of Thermodynamics in Los Angeles it was agreed that any graph with enthalpy as one of its axes would be known as a Mollier Diagram.