∫∫ Sensible Sensibilities

That feeling of relief when walking into an air conditioned building from the stifling heat outside is one of the joys of the modern age. But how does an air conditioner actually achieve this wonderful feat and how much energy does it take? We’ll develop more technical answers in future posts, but for now, we’ll try to understand two fundamental concepts related to optimizing and designing A/C systems: sensible heat and latent heat.

Sensible heat is sensible: smart, reasonable, easy-going. Latent heat is stealthy, ready to smite you with its intense, fiery fury at any given moment. Or, more accurately:

Sensible heat is about temperature changes. Let’s say the air outside is 95 degrees and your shopping mall’s air conditioner is pumping out 55 degree air. Then the sensible heat that the mall air conditioner needs to cool is just the difference between those two temperatures (95-55) or 40 units of cooling. Now let’s say the outdoor air temperature drops to 75 degrees and the mall air conditioner is still pumping 55 degree air into the building. Then the sensible heat change the mall air conditioner needs to cool is simply half as much as was needed before, or 20 units (75-55=20).

Latent heat relates to humidity. It is a measure of the energy stored in the water vapor molecules that fill the air on humid days. Pint for pint, latent heat packs much more punch than sensible heat. The energy needed to heat a gram of water from 80 degrees to 81 degrees is 1 calorie. The energy needed to evaporate a gram of 100 degree water to 100 degree water vapor (steam) is 540 calories. The reason for this difference comes down to molecules. Sensible heat is the energy needed to speed up water molecules. Latent heat is the energy needed to rip apart the bonds attracting the molecules and keeping them liquid. This requires energetic heavy lifting.

Air conditioning has to reduce both sensible and latent heat. Warm, wet air contains many more water molecules than cool, wet air. So air conditioners don’t just lower the temperature from 95 to 55, they remove the energy stored in the evaporated water molecules. Thus, during the cooling process, some water vapor will condense into liquid water.

You’ve seen this effect on a hot day when you take a cold soda bottle out into the humid outdoors. Water droplets condense out of the air and drip down the bottle. The cold bottle surface cools off the hot outdoor air causing the partial pressure of the water vapor to drop so low that some of the water vapor condenses, losing its latent heat. But energy is never lost in thermodynamics, so where does the latent heat go? Into warming up your ice cold bottle. You’ve also seen this: let the soda sit out even a short time in the hot humidity, and it quickly ceases being so wonderfully cold and refreshing.

Latent heat and sensible heat are so fundamental to air conditioning that their relative proportions have their own name: the Sensible Heat Ratio (SHR). The SHR is the sensible heat load divided by the total heat load (sensible heat plus latent heat). The more sensible heat needs to be removed compared to latent heat removed (i.e. the less humidity there is) the higher the SHR. For a typical office building the SHR is 0.85. For other spaces like movie theaters it can be as low as 0.75.

A helpful tool to visualize all this is a psychrometric chart. Psychrometric charts frequently contain a guide that shows the different sensible heat ratio as a slope that can be drawn across the chart. In the chart below the guide is both on the far right and in the semicircle on the top left. The shallower the slope, the greater percentage of the heat load is from sensible heat compared to latent heat.

Psychrometric charts are an overwhelming playground of engineering information. But no matter what your technical level, you can understand the basics by this quick finger exercise. On the bottom axis is temperature. On the main right axis is amount of water vapor. Put your finger on 100 degrees on the bottom axis, then move halfway up the chart. You’re now at about 40% relative humidity. Now move your finger left until you reach the curved left boundary of the chart. Your finger just condensed into liquid water. The amount of water vapor in the air at 100 degrees could not be maintained when you lowered the temperature (moving your finger left). And it had to condense out.

 

Penultimate note

If latent heat packs so much more punch than sensible heat, why is latent heat load only 20-35% of the work an air conditioner has to do (compared to 65-80% for sensible heat load)? The reason is because the percentage (by mole fraction) of water vapor to air – mostly nitrogen and oxygen – is quite low: 1% at 77 degrees and 50% relative humidity. So while latent heat may breathe fiery fury compared to sensible heat’s meek interjections, the sheer mass of air that needs to be cooled compared to water vapor molecules that need to be condensed means that most cooling energy goes into lowering the temperature (sensible heat) not removing humidity (latent heat).

 

Ultimate note

Air does not “hold” water as is commonly misunderstood. It’s true that on hot days there may be more water vapor in the air than on cold days. But you could have water vapor in a vacuum. What is at the heart of water vapor levels in the air is the vapor pressure of water. This vapor pressure scales with temperature. When water is hotter, its vapor pressure is greater than when it is colder. Here’s a good article. (The reason the psychrometric chart curves as it does is precisely because at higher temperatures the total amount of water vapor can be higher than at lower temperatures).

 

Just kidding – one more note

Sensible heat + latent heat = enthalpy, a fundamental parameter in thermodynamics, economizers, and other building controls.

10 Responses to ∫∫ Sensible Sensibilities

  1. Excellent timing. We were just discussing psychrometric charts today and how no one could find a good explanation of them. Thanks!

    Reply
  2. Great review on my undergraduate intermediate thermodynamics. I like the short introduction to the psychometric chart.

    Reply

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