# What's wrong with this way of thinking about greenhouses?

It's a clear day, the sun is shining, warming the ground to 29°. The air is at 26°; a breeze is blowing mixing the air so the temperature is fairly uniform:

Now I section a bit of this scene off with some glass walls:

The walls let light through, so there's no change in the heat moved by radiation. The temperature inside and outside is both 26°, so even without the walls there could be no convection; so, that is not a difference. Likewise for conduction. So, the temperature in the greenhouse stays at 26°.

But I know this can't be right, because when I go to my car on a sunny day, it's sweltering hot inside. What is the error in my way of thinking?

• Yes, there is a problem. Light will pass through the glass, and heats the objects inside. The heat rises up, but the glass slows the transfer of the heat out. The rate is dependent on the difference in temperature. Inside the glass container, it will heat up until the temperature difference is great enough. – LDC3 Dec 3 '14 at 6:28

Glass transmits visible light but it blocks infrared light. This diagram from Wikipedia shows a typical tranmission spectrum for ordinary window glass.

Visible light has wavelengths between 400 and 700nm, so anything with a wavelength greater than 700nm is infra-red. Short wavelength IR is trasnmitted, but above about $\lambda = 2.8\mu\text{m}$ the transmission of infrared out of the greenhouse is greatly reduced. Of course, the glass won't let the infra-red in either, so you might think there would be no net effect. However there is another effect to consider.

The light emitted from the Sun is mainly visible light. The spectrum of the light received from the Sun looks like (again from Wikipedia):

So almost all the light it emits has a wavelength less than $2.8\mu\text{m}$ and the light passes through the glass into the greenhouse where it heats up the soil, plants, and everything else in the greenhouse. All that stuff in the greenhouse now reradiates the energy received from the Sun, but it reradiates it as a black body with a temperature of say 30°C. The spectrum of the light radiated from a black body of this temperature looks like:

I've drawn a vertical red line to mark the point where the glass stops transmitting the light, and anything to the right of this line is not transmitted so it stays in the greenhouse. It's obvious from the graph that most of the energy emitted from the stuff in the greenhouse isn't transmitted so it can't escape the greeenhouse.

And this is why the greenhouse heats up. Most of the energy hitting the greenhouse passes through the glass into the greenhouse, but most of the energy re-emitted by the stuff in the greenhouse can't get through the glass to escape. So there is a net build up of energy inside the greenhouse. The temperature increases until other forms of heat loss like convection balance out the energy received from the Sun.

• Nice answer! Just curious what software you used to produce the blackbody spectrum @ 30 °C. – pentane Dec 3 '14 at 18:39
• @pentane: thanks for the edit - one of those "oops" moments :-). I did the graph in Microsoft Excel. The equation for Planck's law I grabbed off the Internet somewhere. I'd love to claim I keep all these equations in my head, but sadly not. – John Rennie Dec 3 '14 at 18:56

Let me explain it in parts to make it easier for understanding.

In open environment, air/wind keeps conducting the heat from a hotter body (earth in your example) to the cooler surroundings (air far away from this hot earth).

In the absence of this conducting air, the difference between part of earth getting sunlight and part of earth not getting sunlight would continue to increase because one region is getting an input of heat, but not conducting it fast enough.

When you turn up the glass screens on the car doors and then close the doors, you are in fact stopping the inner side of the car from conducting heat through wind. So sunlight (and thus heat) enters the car through the glass screens and it does leave through the glass screens too, but what about the heat absorbed by the inner side? It has an input of heat in the form of sunlight but air cannot conduct the heat away from it to keep it from overheating. It's temperature gradually rises because it is getting far more input of heat than it is radiating through the glass screens.