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How does the color of a car influence its inner temperature change over time when parked outside in windless, hot and sunny regions?

I know what's the common idea about that: black cars are supposed to build up high temperatures faster because black objects absorb radiations instead of reflecting them off. Is it true? And then, what happens during the steady state? Some claim the black car will stay hotter, some others claim it will be the same whatever the color. Do all cars have the same temperature inside in the long run, or are some of them hotter?

I've Googled it but the best I could find was http://phoenix.about.com/od/car/qt/carcolor.htm. It claims to be based upon ~20 articles. But there's not even a mention of absorption or emission spectrums. A priori, a black car could absorb all visible radiations and emit it as infrared while reflecting all of the Sun's infrared. And it's still only qualitative. I've found nothing on Physics stackexchange, the closest being Heat in the car during sunny day.

Community
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peter3265965
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  • "MythBusters used two identical cars, one black the other white and left them both out in the summer heat with thermometers in both. By mid-afternoon the white car had a temperature of 126 °F (52.2 °C), while the black car had heated up to a temperature of 135 °F (57.2 °C), about 9 degrees hotter in the Fahrenheit scale. The explanation was that black paint absorbs heat while white paint reflects it." - https://en.wikipedia.org/wiki/MythBusters_(2005_season)#Biscuit_Bazooka_Spinoff – pentane Jan 13 '16 at 16:42

3 Answers3

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First off, you're right that the temperature depends on what IR wavelengths as well as what visible wavelengths are absorbed (regardless of what color our eyes see).

There's an important rule which states that an object's spectral emissivity, i.e. the rate of emission at a given wavelength is the same as the object's spectral absorptivity. The "trick" is that the overall emission is a function of temperature, while the overall absorption is a function of the incident intensity aka irradiance at each wavelength.

To find out which car gets hotter, you need to run the integral, over spectra, of absorptivity times irradiance and then run a similar spectral integral of the emissivity. Then there's the little problem of specific heat of the car (joules per delta Kelvin), but we can let that be a constant independent of the car's paint color.

And finally, since presumably the car is heating up, you need to calculate the emission integral until the total power (energy/time) radiated equals the incident power, at which point the car's temperature stabilizes.

Carl Witthoft
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  • So, tell me if I get it right: if an object reflects 40% of irradiance, then it absorbs (100-40)/2 = 30% of irradiance, and emits at the same rate? (for a given wavelength) – peter3265965 Feb 03 '14 at 15:34
  • No! Reflectance is completely different from Emittance. While Reflected + Absorbed = 1 (assuming no transmittance), the emissivity is the same as absorptance. So Reflect 40% means Absorb 60%, and so on. – Carl Witthoft Feb 03 '14 at 16:14
  • So, I guess there's no easy, qualitative way of solving this problem. I'll have to do further research on car paint spectral absorbance and do further exhumation of my thermodynamics courses! – peter3265965 Feb 04 '14 at 15:54
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The energy hitting a car in sunshine can be as high as 1300Watts/m^2 in some regions of the world. Reflectance of this energy plays a large role in how fast the interior of the car will be heated. This report covers your question fairly well.

From the abstract:

The design of vehicle air conditioners is based on the maximum cabin (soak) temperature attained when the vehicle is parked on a hot, sunny summer day. Cool colored paints reflect most of the sun’s energy in the near-infrared band (0.7 – 2.5 microns) while offering choice of color in the visible band (0.4 – 0.7 microns). Painting vehicle shells with these cool colors can reduce the soak temperature and thus increase fuel economy by decreasing the vehicle's ancillary load and permitting the use of smaller air conditioners.

......

An experimental comparison of otherwise identical black and silver compact sedans indicated that increasing the solar reflectance rho of the car's shell by about .5 lowered soak temperature by 5-6 C .Thermal analysis predicts that the air conditioning capacity required to cool the cabin air in the silver car to 25C with 30 minutes is 13% less than required in for the black car.

And their summary

We measured the solar spectral reflectance and thermal emittance of over 180 car coating samples obtained from two automotive coating manufacturers: BASF Automotive Coatings, and PPG. These samples included both production colors and prototype color colors. Solar reflectance, visible reflectance, near-infrared reflectance, and color coordinates (CIELAB *L, *a and *b) were computed from solar spectral reflectance. Solar reflectance index (SRI) was computed from solar reflectance and thermal emittance. Our measurements verified that the prototype cool colors did generally exhibit solar reflectance exceeding visible reflectance. Solar reflectance ranged from 0.04 (conventional black) to 0.70 (conventional white), with many cool colors ranging in solar reflectance from about 0.20 to 0.50. All coated samples exhibited high thermal emittance (0.82 - 0.95).

It is the reflectance that makes the difference between dark colors and light colors and the proposal is to used this knowledge to reduce the air conditioning load of cars.

endolith
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anna v
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The reason your car gets hot on a sunny day has little to do with the color of the paint. It is due mostly to the greenhouse effect of the glass.

The greenhouse effect happens when light with higher energies (visible light for example) passes through the glass and is absorbed. The absorbed energy causes the interior parts of the car to heat up and emit in the infrared, but this wavelength is reflected by the glass creating a one way energy valve. This effect depends on the air not being able to escape so that the heat is not taken away by convection. The image below from this hyperphysics article illustrates the effect.

Greenhouse Effect

Glorfindel
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Chris Mueller
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  • While this is accurate, why not answer the OP's question by positing two cars with common interior and common glass type, so the only variable is the paint color? – Carl Witthoft Feb 04 '14 at 12:51
  • You're right @CarlWitthoft. All I can infer from your answer, and particularly from the sentence "has little to do with the color of the paint" is that temperature will change the same way whatever the color of the car paint. – peter3265965 Feb 04 '14 at 15:44
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    @peter3265965 I took your question as a practical one. The point of my answer is that the temperature of the car is due to energy which gets in through the windows and is not released. The temperature will therefore be nearly identical regardless of the color or type of the paint. To be honest, any answer about how the paint effects the temperature needs to account for more than the color; for example what type of clear coat covers the paint and what is the metallic content. – Chris Mueller Feb 04 '14 at 16:56
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    But energy does not come in through the windows only!! The car roof is not insulated, just some metal. The color is important in reflecting the energy so less is absorbed. Greenhouses (the real ones) get hotter than outside temperature because of lack of convection not because of the glass. The difference of a glass cage to the land surrounding it is that there is no convection, otherwise the same energy is absorbed. In the case of the car the part coming from the windows is the same, but the part coming from the roof and sides can have 50% or more depending on reflectivity. – anna v May 10 '14 at 10:50
  • @annav Greenhouses get hotter because the glass transmits visible light but doesn't transmit infrared light as well – endolith Apr 26 '18 at 19:47
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    I am comparing two volumes next to each other. If you open the sides of the green house it will come to the ambient temperature not because of unimpeded infrared radiation, but because of convection. Impeded infrared traps energy, yes. – anna v Apr 27 '18 at 03:43