Temperature behavior over time of black or white cars in hot, sunny regions

Question

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.

Answer 1

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.

Answer 2

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.

Answer 3

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.