The latent face of the heat

The latent face of the heat

The press release describes the results of the work of Paweł Żuk, who conducts a project Stationary states out of equilibrium in various physical systems under PD2PI. He studies a special case of thermodynamic nonequilibrium state: a stationary state, which a physical system can achieve e.g., under a constant external forcing. Paweł Żuk is interested in finding and examining an extreme principle that characterizes such system. He focuses on the energy of the system instead of the entropy. He aims to study three systems in stationary state under external forcing that have different underlying physics: Fermi-Ulam-Pasta-Tsingou model, gas flow in a channel with an obstacle and ionic solution in the vicinity of the oscillatory electrode.


Science is driven to "know". We want to know how everything works, how things happen and wonder "what if" and "why". Even measuring the temperatures on a mixture experiment with hot and cold water or hot and cold gas can lead to an interesting observation. Heating is essential to increase an object's temperature, and looking at the sudden cut-off of the heat source uncovers fascinating effects. Recently, scientists from the Institute of Physical Chemistry Polish Academy of Sciences have confirmed the Mpemba effect in an ideal gas and revealed the unknown face of the heat. Their discovery starts by considering a simple system with a well-defined temperature distribution: the pipe filled with the ideal gas, excessively heated at one end. Let's take a look closer at their findings.

We live in an energy-bound civilization, where energy means everything. House heating, car engines, or photovoltaics operation are closely related to transferring one type into another. For example, burning fossil fuel inside a furnace releases chemical energy, which was deposited into chemical bonds thousands of years ago by plants, in the form of heat and radiation. Likewise, our bodies constantly convert chemical energy into heat released to the environment and work performed by our muscles. No matter what we do, heat accompanies us every day. Microscopically, heat transfer occurs from a mismatch of the thermal, jiggling motion that every atom experiences. Heat will flow in the physical system until all atoms jiggle alike.

For example, we measure the temperature with a thermometer. This device translates the jiggling motion of atoms into well-defined numbers: the temperature scale. The readout will change as long as the motion of atoms in the body and the thermometer is not alike. Once they move similarly, we call this situation a state a thermal equilibrium and give it a unique number: temperature. Similar happens inside the bulk of liquids or gases: the heat transfer progresses due to the uneven collisions between hot molecules and cold ones.

Let's look at the gas-filled pipe, where one closed end is in constant contact with the hot environment and the other closed end with the cold environment. The temperature will change along the pipe to smoothly connect both sides. Because of the persistent mismatch of the thermal motion along the pipe, heat flow is established from the hot end to the cold one. If there is a thermal motion, can we imagine the speed of heat? Furthermore, what if the heat transfer is instantaneously stopped at the hot end? The most obvious answer would probably be – quite fast, the gas reaches the thermal equilibrium. Indeed, as the heat transfer stops, it happens. Nevertheless, it does not occur as most scientists expected.

Recently, researchers from the Institute of Physical Chemistry, Polish Academy of Sciences, led by prof. Anna Maciołek focused on the outflow of energy in the form of heat from the gas, having a nonuniform temperature initially. The temperature profile resulted from a constant energy flow supplied to the gas.

Scientists analyzed in detail what happens when the energy flux is closed instantly. In addition to the gentle slowing down of thermal motion due to consecutive interparticle collisions, known as heat diffusion, they discovered a violent, rapidly spreading change in the state of the gas.

The front moves through the gas with the speed of sound and leaves the lower temperature behind. Even more surprisingly, the pressure is lowered behind the front; therefore, the front propagates upstream of the pressure gradient. As a result, long before the diffusive changes reaches the cold wall, the gas cools by some amount wherever the front passes. Moreover, the front appears to be a direct witness of the vanishing heat flux, which reveals how fast the heat travels.

Studying a longer time scale, they asked will the system heat up as quickly as it cools down. Instead of turning off the heat influx at the hotter end, they turned off the heat outflux at the colder end of the pipe. Researchers found that it takes longer to equilibrate the gas with the hotter end.

Dr. Żuk, the first author of the work, remarks: “If the temperature gradient in the initial state is the same, then the energy difference between the steady state and the final equilibrium controls the relaxation time, i.e., the smaller this difference is, the faster is the process. In the heating/cooling comparison, more energy is needed to reach equilibrium with the hotter end than with the colder one. The reasoning along similar lines leads to the Mpemba effect".   

The Mpemba effect is a general name for the counterintuitive phenomenon reported by Mr. Mpemba: out of two objects that initially have different temperatures, placed in a cold environment, the hotter one may cool down first. Mr. Mpemba reported a comparison between the freezing times of hot and cold water.

"In the case of gas with underlying heat flux, we proved the accelerated cooling of the hotter object is the consequence of the relationship between the amount of energy stored in the steady state and the strength of the heat flux flowing through the system in this state." – claimed dr. Żuk.

These findings show how much there is to unravel, even in the fields that seem to be known. From Greek philosophers like Lucretius, who claimed: "No rest is allowed the elemental-atoms moving in space," through the well-defined concept of heat to the finding how fast the thermal energy is being transferred. By now, thanks to the findings presented in the paper published in Physical Reviews E by researchers from IPC PAS, the Mpemba effect in the ideal gas was proved, and that heat travels with the speed of sound.

This work  was done within the project that has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 847413 and was a part of an international co-financed project founded from the program of the Minister of Science and Higher Education entitled “PMW” in the years 2020–2024; Agreement No. 5005/H2020-MSCA-COFUND/2019/2.

“Transient dynamics in the outflow of energy from a system in a nonequilibrium stationary state”
Paweł J. Zuk, Karol Makuch, Robert Hołyst, and Anna Maciołek
PHYSICAL REVIEW E 105, 054133 (2022) 1012
DOI: https://doi.org/ 10.1103/PhysRevE.105.054133