The physics of Spain's controversial air-con decree

The Government of Spain published a decree earlier this week that prevents air-conditioners from being set at a temperature lower than 27º C in the summer in an effort to lower energy consumption and wean the country off of natural gas pumped from Russia.

A Twitter thread by Euronews compared the measure to one by France, to keep the doors and windows of air-conditioned spaces closed. However, the two measures are not really comparable because the France’s measure is in a manner of speaking shallower, because it doesn’t go as far as thermodynamics allows us. Instead, Spain’s move is comparable to one that Japan instituted a couple years ago. Some basic thermodynamics here should be enlightening.

Let us consider two scenarios. In the first: Air-conditioners operate at different efficiencies at different temperatures. From about five years ago, I remember the thermodynamic efficiency variation to be around 10% across the range of operating temperatures. Also note that most air-conditioners are designed and tested to operate at or near 23º to 25º C – an ambient temperature range that falls within the ideal ranges across most countries and cultures, although it may not account for differences in wind speed, relative humidity and, of course, living conditions.

So let’s say an air-conditioner operates at 55% efficiency when the temperature setting is at 27º C. It will incur a thermodynamic penalty if it operates at a lower temperature. Let’s say the penalty is 10% at 20º C. (I’ve spelt out the math of this later in this post.) This will be 10% of 55%, which means the thermodynamic efficiency at 20º C will be 55% – 5.5% = 49.5%. Similarly, there could be a thermodynamic efficiency gain when the air-conditioner temperature is set at a higher 32º C instead of 27º C. This gain translates to energy saved. Let’s call this figure E_S (for ‘energy saved’).

In the second scenario: the air-conditioner works by pumping heat out of a closed system – a room, for example – into the ambient environment. The cooler the room needs to be, the more work the air-conditioner has to undertake to pump more heat out of the room. This greater work translates to a greater energy consumption. Let’s call this amount E_C.

Now, the question for policymakers is whether E_S is greater than E_C in the following conditions:

1. The relative humidity is below a certain value;
2. When the room’s minimum temperature is restricted to 27º C;
3. The chances of thermal shock; and
4. The given strength of the urban heat-island effect.

Let’s cycle through these conditions.

1. Relative humidity – The local temperature and the relative humidity together determine the wet-bulb temperature. As I have explained before, exposure to a wet-bulb temperature greater than 32º C can quickly debilitate humans, and after a few hours could even lead to death. But as it happens, if the indoor temperature is 27º C, the wet-bulb temperature can never reach 32º C; even at 99% relative humidity, it reaches a value of 26.92º C.

2. 27º C limit – The operating range of the sole air-conditioner in my house is 18º to 32º C when the ambient temperature is 18º to 48º C. In thermodynamic speak, an air-conditioner operates on the reverse Carnot cycle, and for such cycles, there is a simple, fixed formula to calculate the maximum coefficient of performance (CoP). The higher the CoP, the higher the machine’s thermodynamic efficiency. (Note that while the proportionality holds, the CoP doesn’t directly translate to efficiency.) Let’s fix the ambient temperature to 35º C. If the indoor temperature is 20º C, the max. CoP is 1.33, and if the indoor temperature is 27º C, the max. CoP is 3.37. So there is an appreciable thermodynamic efficiency gain if we set the air-conditioner’s temperature to a higher value (within the operating range and assuming the ambient temperature is greater than the indoor temperature).

3. Thermal shock – The thermal shock is an underappreciated consequence of navigating two spaces at markedly different temperatures. It arises particularly in the form of the cold-shock response, when the body is suddenly exposed to a low temperature temperature after having habituated itself to a higher one – such as 20º C versus 40º C. The effect is especially pronounced on the heart, which has to work harder to pump blood than it did when the body was in warmer surroundings. In extreme cases, the cardiac effects include vasoconstriction and heart failure. Cold-shock response is most relevant in areas where the ambient conditions are hot and arid, such as in Rajasthan, where the outdoors routinely simmer at 40-45º C in the summer while people intuitively respond by setting their air-conditioners to 18º C or even lower.

4. Urban heat islands – When a single air-conditioner is required to extract enough heat from a room to lower the room’s temperature by 15º C instead of by 8º C, it will consume more energy. If its thermal efficiency is (an extremely liberal) 70%, 30% of the heat it consumes will be discarded as waste heat back into the environment. Imagine a medium-sized office building fit with 25 such air-conditioners, a reasonable estimate. During the day, then, it will be similarly reasonable to conclude that the temperature in the immediate vicinity of the building will increase by 0.5º or so. If there are a cluster of buildings, the temperature increase is bound to be on the order of 2º to 3º C, if not more. This can only exacerbate the urban heat-island effect, which adds to our heat stress as well as degrades the local greenery and faunal diversity.

Take all four factors together now and revisit the Spanish government’s decree to limit air-conditioners’ minimum operating temperature to 27º C during summer – and it seems entirely reasonable. However, a similar rule shouldn’t be instituted in India because Spain is much smaller and has lower meteorological and climatological variations, and also has less income inequality, which translates to lower exposure to life-threatening living conditions and better access to healthcare on average.