What Determines the Temperature Inside My Car When Parked in the Sun?

[Char. Limit]

I'd post this as a homework question, but I don't even have a real basis for it, and what I want is an equation.

So my car sits out in the sun, and this causes the air inside the car to get hotter. My question is, what equation determines the inside temperature of a car out in the sun? I'd assume it has something to do with radiation, but I have no idea.

 

[xts]

Not that easy. Generally in the equilibrium state, the car should remit the same amount of heat as it absorbs.
Absorbed heat is relatively easy to calculate: you must integrate over light frequency the energy flux of sun light (Planck's law) times emissivity of your car paint.
Remited energy cosist of two parts: first is radiation (again - integrate paint emissivity times Planck's distribution at the car temp).
Second is pretty difficult to predict teoretically - heat transferred to the air, as it depends not only on ambient air temperature, but also on air flow around your car, which in turn depends on wind speed and car geometry.

If you want to be more precise, you should separately compute the heating of black cockpit with greenhouse effect of the windshield. I am not brave enough to start such calculations...

 

[LostConjugate]

It is the windows. The material in your car receives energy from the sun in UV, Visible, and near IR radiation. The objects in your car heat up. They re-emit radiation with a longer wave length. This radiation is absorbed by your windows and some of it is radiated back into your car. Trapping of long wavelength thermal radiation is what makes your car so hot. The Greenhouse effect.

Those metallic visors reflect more of the radiation as shorter wavelength and prevent your car from heating up. Only 4% of visible radiation is reflected from glass, vs 50% of thermal radiation.

I don't know about an equation...

 

[xts]

Pure greenhouse effect is relatively easy: just balance incoming and outgoing energy.
Each of them you may compute integrating Planck's distribution with emissivity of the cockpit and (1-reflectivity of the window).

But - even if you use alufoil to protect car from greenhouse heating, it is still much hotter than ambient air (at least if it is dark painted). Greenhouse effect may be responsible for half of the heating, but direct radiative heating is also important.

 

[LostConjugate]

But - even if you use alufoil to protect car from greenhouse heating, it is still much hotter than ambient air (at least if it is dark painted). Greenhouse effect may be responsible for half of the heating, but direct radiative heating is also important.

There is either a lot of insulation between the fiberglass body or a huge free air gap (like near the engine bay or rear bumper).

I think most of it comes from greenhouse.

 

[Char. Limit]

If it helps, the car is dark green.

 

[xts]

If it helps, the car is dark green.

Like mine Fortunately usually I may park in shadow

 

[SteamKing]

Most car bodies are made of steel. Since steel is a relatively good conductor of heat, car bodies painted a dark color are most efficient at trapping solar radiation.

 

[mrspeedybob]

This sounds like a good application for good old fashioned experimentation. You'll need equipment to log sunlight intensity, inside air temperature, outside air temperature, wind speed, humidity, and whatever other variables you want to include. Play around with your data and your equation until there is a good match between them and then try to use your equation to make predictions and see how accurate you are.

 

[LostConjugate]

Most car bodies are made of steel. Since steel is a relatively good conductor of heat, car bodies painted a dark color are most efficient at trapping solar radiation.

Steel sounds kind of heavy. I think your average commuter is made out of fiber glass, plastic, and aluminum.

 

[Neandethal00]

I'd post this as a homework question, but I don't even have a real basis for it, and what I want is an equation.

So my car sits out in the sun, and this causes the air inside the car to get hotter. My question is, what equation determines the inside temperature of a car out in the sun? I'd assume it has something to do with radiation, but I have no idea.

Here is another approach you can use. But note, this is no way the exact solution to the problem because there are many ways heat can enter a car.

Think of rise in temperature inside a car is the temperature of heated air trapped inside. At first find amount of heat entered into car through metal top and glass sides by conduction using
Q = kAt(To-Ti)/d
Q is the amount of heat. Any physics text has explanation for other letters.
Then find mass of the air trapped inside volume of the car.
m = Volume *(air density).

Then calculate heat absorption by air inside car using

Q = mc(T2-T1)

c = specific heat of air.
T1 = starting temperature of air
T2 = solve for T2 as the final temperature of heated air inside.

As you can see it all depends on correct computation of Q. In this case I have oversimplified.

 

[mrspeedybob]

Steel sounds kind of heavy. I think your average commuter is made out of fiber glass, plastic, and aluminum.

The average commuter in your neighborhood must be a Corvette.

Take a magnet, wrap it in plastic so you don't scratch anybodies paint, and go stroll through a parking lot. Excluding bumpers, you'll find 90% or better of all car body panels are steel. The exceptions are going to be some sports cars and Saturns.

Steel may be heavy, but it is strong and cheap. Often car makers will minimize the weight by creating hollow structures and compound curved surfaces.

 

[willem2]

Pure greenhouse effect is relatively easy: just balance incoming and outgoing energy.

But - even if you use alufoil to protect car from greenhouse heating, it is still much hotter than ambient air (at least if it is dark painted). Greenhouse effect may be responsible for half of the heating, but direct radiative heating is also important.

Actually, the main function of the windows is to stop convection. The windows do not block much heat from escaping, because the heat is conducted from the inside to the outside of the windows, and then reradiated.
The same goes for real greenhouses BTW. This has been tested with rock salt instead of glass, which will let IR pass through.
http://www.wmconnolley.org.uk/sci/wood_rw.1909.html"