### Why cold clothes feel damp

Our new apartment has laundry in the building, but in a room that can only be accessed by going outside and then in through a separate entrance. The result in winter is that on its way back, a hamper full of freshly dried clothes will acquire a layer of cold clothing around its warm cozy center. When I feel this cold clothing later, part of my brain says, “Oh, no! It didn’t get dry!”

Partly, that thought is from experience: you can tell whether clothes are ready to come out of the dryer by whether the heat has gone from evaporating the water to warming the clothes, so if they don’t feel warm yet it’s because there’s still moisture present. But the cold clothes also just feel damp, even though they’re not. That got me wondering: why do cold clothes feel damp? The answer has to do with how we experience temperature at all.

Anyone who has sat on a toilet seat in a cold house has probably experienced some part of this continuum of how warm the seat feels, based on what it’s made of:

• Porcelain: coldcoldcold
• Plastic: a bit chilly
• Wood: kind of warm. Also, eww.

The difference between these seats isn’t their actual temperature: they’re all approximately the same temperature as the ambient air. What differs is how easily they conduct heat away from your body, a property called thermal conductivity.

When two objects of different temperatures (your butt and the toilet seat) come into contact via some intermediate substance (the surface of the seat), the formula for the rate Q at which heat flows from the hotter object to the cooler one is

$Q = \Delta T\cdot K \cdot \dfrac{A}{L}$

where $\Delta T$ is the temperature difference, K is the thermal conductivity, A is the surface area of contact, and L is the thickness of the material. The factors that I want to focus on are those first two: the rate of heat flow is proportional to the temperature difference, yes, but also to how thermally conductive the material is. My guess is that when we think we are sensing temperature, we’re actually sensing the rate at which heat is leaving our bodies, which depends equally on those two factors.

For example, here are some approximate thermal conductivities of common materials:

• Air: 0.03
• Wool: 0.07
• Wood: 0.1
• Cotton: 0.2
• Water: 0.6
• Concrete: 0.8
• Porcelain: 1.5
• Steel: 50
• Brass: 100
• Aluminum: 200

Since water is about three times more thermally conductive than cotton, if I feel some damp clothing that is 20 degrees cooler than my hand, it will register about the same temperature-feeling as dry clothing that is 60 degrees cooler than my hand. That’s why the winter-chilled dry clothes feel like they’re wet!

In fact, thermal conductivities tend to vary over a much wider range of orders of magnitude than most of the temperature differences we encounter, so you could even claim our touch sense of temperature is mostly a touch sense of thermal conductivity, and is more useful for distinguishing materials than temperatures.

(Incidentally, this is the same reason the rivets and zippers on freshly dried jeans feel so hot compared to the denim: they’re not actually any hotter in terms of temperature, but the high thermal conductivity of metal means they’re very efficient at transferring their heat into your skin!)

How about you — do you have any stories of your sense of temperature led astray by thermal conductivity? Do our other senses perceive something slightly different from what we think they do? I’d love to hear your thoughts in the comments!

## 4 thoughts on “Why cold clothes feel damp”

1. I learned a lot there 🙂 I’m glad I know more about thermal conductivity and how it works.

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2. Fun! But I wonder if something is hiding under the carpet in the formula, namely the $L$ term. What is the material of which we’re taking the thickness in your toilet seat example? The formula seems to me to be about rate at which thermal energy passes through an insulator when the temperatures on both sides are held fixed? In this example I think one should also take into account the thermal capacity of the seat material (how much the temperature changes for a given amount of energy absorbed). For example, if the seat material has very high conductance but very low thermal capacity, then it would almost immediately reach your body temperature, and no longer feel cold. Maybe one can derive a formula by slicing up the seat into layers, applying your formula and the thermal capacity to each layer, then letting the layer thickness go to zero?

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1. Thanks! Yes, I wondered what to do about that L term too. Should we combine it with the temperature as $\Delta T/L$ and think of it as an approximation to the derivative? How should we interpret that when two materials of different temperatures come into contact? I would be interested in running some simulations with the heat equation and seeing how the capacity and conductance together affect the heat transfer rate.

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