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| Fig. 1: Entropy of mixing; mechanism differs from heat flow, but underlying point is same - systems evolve toward higher-entropy states. (Source: Wikimedia Commons) |
To understand cooling, we start with a simple fact: heat flows naturally from hot to cold. Cooling is fundamentally the act of forcing heat to flow in the wrong direction - from a colder place to a warmer one - and physics demands that doing this always costs energy. Temperature tells us how hot something is, whereas heat is the actual energy that moves and spreads. If you put a cold space in contact with a warmer environment, the cold space will warm on its own; nothing has to push heat inward because the system naturally moves toward thermal equilibrium. The same idea appears when two gases mix spontaneously - once a divider is removed the particles scramble as seen in Fig. 1.
This mixing serves as an analogy for thermal contact: when a cold region touches a warmer one, energy spreads, the system moves toward equilibrium, and entropy increases. The entropy change (ΔS) associated with heat energy (Q) dumped at temperature (T) is: [1]
But knowing the entropy change is only part of the story - we also need to understand where the energy comes from. The First Law of Thermodynamics tells us that energy is conserved. And to keep something cold, we must continuously remove heat and export entropy to the surroundings. And the only way to undo entropy is by doing work. For any cooling system, the heat expelled to the surroundings must equal the heat removed from the cooled space plus the work supplied to drive the process:
In practice, that work usually comes in the form of electrical energy. This physical reality sets the stage for comparing cooling technologies: they all face the same thermodynamic constraint, and the question is never whether one can avoid paying for entropy removal, but how efficiently it performs that task.
Because cooling means pushing heat from cold to hot, the natural question is: what is the best any cooling system could ever do? Physics answers this through the Carnot limit. The relationships above allow us to connect cooling directly to the Carnot limit.
If we take the first law of thermodynamics, energy is conserved. Heat rejected to the environment equals the heat removed from the cold space plus the work we supply:
For a perfect, idealized system (where no entropy is created), the entropy carried out must equal the entropy removed:
Substituting the first-law expression Qhot = Qcold + W into the entropy balance we obtain:
Solving for the minimum work required by multiplying both sides by Thot we then obtain:
Rearranging we obtain finally:
This expression tells us that the minimum work required to pump heat depends only on the temperature difference, not the machine design. We can then use this to think about the best performance any cooling system could ever achieve. The coefficient of performance (COP) is the ratio of useful cooling (Qcold) delivered relative to the work (W) required to do it:
Substitute the expression we derived above for W and the Qcold terms cancel, giving:
This is the Carnot limit for cooling - the best any system can ever do in theory. The numerator represents the useful heat removed from the cold space, and the denominator is the temperature lift - how far in temperature the system must push that heat. Real systems always perform worse, because real processes generate entropy. Every cooling technology, present or future, is bounded by this same physical limit.
Most cooling systems today use the vapor compression cycle, where a refrigerant is repeatedly evaporated and condensed while a compressor supplies work to pump heat from indoors to outdoors. The compressor raises the refrigerants pressure and temperature, the outdoor coil rejects heat to the environment, and an expansion valve drops the pressure so the refrigerant can absorb heat again inside. Its performance is judged by how close it comes to the Carnot limit shown above. Across a range of vapor-compression applications - from residential air conditioning to commercial refrigeration - COPs can vary between ~2 and 5, depending on factors such as ambient conditions, system design, and intended use. [2,3] Corresponding estimated Carnot efficiencies can range from as low as 15 - 20% to approximately 40%+ in more optimized contexts based on differences in typical operating temperatures and system designs. [2,3] These systems today are mature, optimized, and produced at scale, which means they already sit relatively close to the thermodynamic ceiling while being low-cost and highly reliable.
Elastocaloric cooling instead uses shape-memory alloys like nickel-titanium (NiTi) that heat up when mechanically stressed and cool when unloaded as they switch crystal phases. When cycled, the alloy can absorb heat from a cold space and reject it to a warm space. Unlike vapor compression systems, the working material in this system is a solid rather than a refrigerant fluid; however, most practical designs still would use a secondary heat-transfer fluid to move heat to and from the alloy. Laboratory demonstrations have shown material-level COPs of ~2.7-3.0, and analyses suggest that if the unloading heat could be fully recovered, system COPs between ~3.7 and 11.8 might be possible. [2] Here, material-level COP refers to the idealized performance of the alloy itself in lab conditions, typically measured without accounting for real-world system losses like heat transfer inefficiencies, fluid pumping, or incomplete recovery of heat during unloading. In contrast, full-system COP includes these losses and is a better reflection of practical device performance. Because elastocaloric systems rely on a solid working material, heat transfer occurs primarily by conduction and some heat can leak back through the material, whereas vapor-compression systems use flowing fluids to carry heat away by convection, which is generally more effective at limiting this leakage. It is important to note that while the DOE report lists COP values across systems, these numbers are not directly comparable because they are measured under different experimental conditions and temperature lifts. A true apples-to-apples comparison would require expressing each systems performance as a percentage of the Carnot COP, and such %-of-Carnot data is not yet reported for elastocaloric systems.
More recent DOE updates report only early prototypes and technology readiness levels (TRL) around TRL 3-4, meaning bench-scale testing with no commercial systems yet. [4] The largest practical challenge is durability: elastocaloric devices must survive tens of millions of stress cycles, and the DOE notes fatigue and system complexity as key barriers to scaling. [4]
There is no penalty or bonus for choosing refrigerant compression versus stressing a solid - the Carnot limit applies equally. What matters is how close each approach gets to that limit in practice, and how much it costs to do so. Vapor compression already delivers large-scale COPs near half the ideal limit at low cost. Elastocaloric cooling has shown promising material-level results, and DOE projections suggest it could match or exceed vapor-compression efficiency if durability and engineering challenges are solved. But at present, elastocaloric systems remain laboratory demonstrations without system-level performance that surpasses vapor compression or have a proven cost advantage. [4] In other words, the physics does not rule out elastocalorics - but until measurements show higher COP in real systems and materials survive long-life cycling at reasonable cost, vapor compression remains the benchmark cooling technology.
© Zac Maslia. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
[1] Y. A Çengel and M. A. Boles, Thermodynamics: An Engineering Approach, 8th Ed. (McGraw-Hill, 2014).
[2] W. Goetzler et al., "Energy Savings Potential and RD&D Opportunities for Non-Vapor-Compression HVAC Technologies," U.S. Office of Energy Efficiency and Renewable Energy, March 2014.
[3] D. R. et al., "The Prospects of Alternatives to Vapor Compression Technology for Space Cooling and Food Refrigeration Applications," Pacific Northwest National Laboratory, PNNL 19259, March 2010.
[4] W. Goetzler et al., "Energy Savings Potential and RD&D Opportunities for Commercial Building HVAC Systems," U.S. Office of Energy Efficiency and Renewable Energy, December 2017.
