# Why clothes keep us warm?

I want to understand why clothes keep us warm. I understand that they reflect back thermal radiation and also trap air thus significantly reducing cooling due to thermal convection. My question is, do they keep us warm also due to reduced thermal conduction? Searching over the internet, the usual answer is yes. However, this seems contradictory to the fact that air has lower thermal conductivity than wool. This last fact seems to indicate that if (big if here but interesting thought experiment) there was no thermal radiation, no gravity (thus no thermal convection) and no air currents (which would push away warm air near my body), then clothes would not help with keeping us warm.

• as long you don't move and prevent convection, maybe, but you would be a double glazing Commented May 28 at 21:53

Your thought experiment is to have only thermal conductivity to draw heat away from someone. In one case, the thermal layer is air. In another, it is a layer of clothing.

This is a problem with a thermal resistor between two bodies at different temperatures, $$T_s$$ as the person and $$T_a$$ as the (external) air. The net heat flow $$\dot{q}$$ with a thermal resistor $$R = L/k A$$ is

$$\frac{\dot{q}}{A} = \frac{k(T_s - T_a)}{L}$$

With the same thickness $$L$$ of either air or cloth, and with the same "air" temperature $$T_a$$ at the end point of the thickness $$L$$ away from $$T_s$$, the material with the higher thermal conductivity $$k$$ will have a higher heat flux (flow per unit area $$\dot{q}/A$$).

In summary, yes ... when radiation and all forms of convection (natural and forced) are eliminated, and when the bulk air immediately at a distance $$L$$ away from us remains at the same temperature in either case, since $$k_{air} < k_{cloth}$$, we will feel warmer when we would stand naked in air than to put on a (tight) layer of clothes in the same conditions.

Air next to your skin gets warm and then carries heat with it as it moves away. Reducing this is key. Down does it by trapping air between feathers.

One cotton shirt is very little help on a cold day. Two cotton shirts are surprisingly warm.