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Windows and greenhouses

Heat and matter · level 7, lesson 5 of 6

A question to start

Plants need light. A greenhouse on Mars would let sunlight in, but its glass would also let heat out all night. Does it gain more than it loses?

The idea

Glass lets visible light through, but absorbs most infrared. Sunlight comes in, warms the plants and soil, and the infrared they give out cannot easily get back through the glass. That traps heat: the greenhouse effect of a real greenhouse (along with stopping the warm air blowing away).

But glass is a fairly good conductor, so windows leak heat. More panes, with gaps of still gas between them, cut the loss:

Glazing U-value, W/(m² K), about
Single pane 5.8
Double 2.8
Triple 1.0
sunlight ininfrared trappedheat leaks

Worked examples

1. Loss through triple glazing on Mars. Inside 20 °C, outside −59 °C: \(1.0 \times 79 = 79\) W per m², every hour of the sol.

2. Gain from the Sun. From the energy topic, a flat surface near the equator gets about 130 W per m² on average over a clear sol. Suppose the glass lets 70% through: about 91 W per m².

A triple-glazed greenhouse, per m², averaged over a sol Mars Earth
Sunlight let in, clear sky about 91 W about 230 W
Heat lost through the glass about 79 W about 5 W
Left over about 12 W about 220 W

On Earth (using the same 70% of 325 W/m² and 15 °C outside) a greenhouse gains plenty. On Mars it barely breaks even on a clear sol, and loses badly at night and in dust storms. Mars greenhouses would need insulated covers at night, or would grow plants under lamps instead.

3. With a night cover. Suppose an insulating cover cuts the loss to 0.3 W/(m² K) for the 12 h of night: the loss drops to about \((79 + 24)/2 \approx 52\) W per m² on average.

Try it

  1. Why does glass trap heat in a greenhouse?
  2. Find the loss through 20 m² of double glazing with 79 K across it.
  3. Why do more panes cut the heat loss?
  4. Why might a Mars base grow food under lamps rather than in greenhouses?
Answers
  1. It lets visible sunlight in but absorbs the infrared the plants and soil give out, and it stops warm air blowing away.
  2. \(2.8 \times 20 \times 79 = 4{,}400\) W.
  3. Each gap of still gas adds thermal resistance.
  4. Weak sunlight and huge heat loss mean a greenhouse gains little; lamps in an insulated, buried room may cost less energy overall, and work through dust storms.

Common mistake

"More glass means more warmth." Glass lets light in but also leaks heat. On Mars, with 79 K across it, large glass areas can lose more heat than the sunlight brings.

Where it leads