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I understand that one way to tell how much a liquid will be heated up by a remote heat source is by looking at its color. I assume clear and colorless heats up least, then white, other colors and last black liquids will heat up the most. ( Is this right and can more detail be added?)

However I don't understand the physics well enough to answer this simple sounding question. What other factors except for visible color affect how much the liquid will be heated?

If it is possible to give quantitive figures that would be great.

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The colour is sort of a side effect. Liquids that absorb more of the available wavelengths will heat up more - black absorbs most, although if the available light is only at certain wavelengths, then the absorption at those wavelengths is the most important factor.

For our sun, the spectrograph looks like this (from disclose.tv) so while it looks yellow, you can see that there is significant energy between about 500 and 600nm so this is where a liquid can most efficiently absorb energy.

enter image description here

But there is energy off both sides of the visible spectrum, and despite the intensity dropping off towards 400nm, this radiation is higher energy.

Also important is how fast energy is redistributed, through conduction, radiation and convection. From a radiation perspective, the colour may impact how much heat is re-radiated. This energy is likely to be at a lower wavelength than the incoming energy so the optimum colour for avoiding radiating this energy will be different.

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I am assuming the heat source is the sun in natural daylight. Are there examples of liquids with the same visible color that would heat up at different speeds or even clear, colorless liquids which absorb more non visible wavelengths from the sun? –  marshall Jun 5 '13 at 16:53
    
Is there known math for calculating the total net heat change? –  marshall Jun 5 '13 at 17:15

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