How would a solid shell surrounding Earth affect the climate?

Question

(First time posting on worldbuilding, be gentle!)

For reasons currently unimportant, Earth has been encased in a solid shell which is for all intents and purposes completely invulnerable. The shell cannot be damaged by (for example) meteor strikes or large explosions, and does not allow radiation to pass through it in either direction. By this I mean electromagnetic radiation (including light), and heat. All such radiation is reflected by the inner surface of the shell. The shell appeared in a relatively short time, taking a matter of days or weeks to be placed around the planet.

Assume that through some means the shell remains steady about the Earth and there is no chance of it drifting and colliding with the planet. It is positioned high in the atmosphere, somewhere in the exosphere (roughly 600-700km up). If this conflicts with any existing satellites then they can be assumed to have been destroyed. Then my question is:

How would this affect the climate?

Specifically: without the sun, would there still be wind and other types of weather? How would the temperature be affected over time?

Answer 1

Without sunlight, all photosynthesizing plants would die. Then all animals would die a little while later. Most fungi are dependent on the presence of energy-rich (decaying) plant matter, so they may thrive for a long time and then die out after exhausting their food source. It's unlikely that anything other than bacteria can switch their energy source to new chemical sources, leaving only a bunch of bacteria and a few isolated cave-dwelling populations. The composition of the atmosphere will change due to the rotting of all that dead stuff and the bacteria thriving on it. However, due to the lack of sunlight, this will not affect things greatly anymore.

Without day and night, winds will mostly cease (no more thermals, only a slight breeze from oceans currents at most). The ice caps will slowly melt, equalizing the temperature across the globe, thus stopping most ocean currents. The planet will become very still and mostly covered by water. Over many thousands of years, the remaining bacteria will evolve to a new balance, resembling a ridiculously huge cave. If you're lucky, some of the cave-dwelling animals manage to survive on the surface and spread out a little, but most of the planet is likely too toxic for them, since they evolved in very fragile environments, and even those caves might have been dependent on oxygen-containing water coming from the surface.

A few thousands to millions of years more will see rising temperatures as the heat from the planet's core slowly spreads now that the planet is not able to radiate its heat anymore. This is estimated at 43-47 Terawatts over the whole planet, both from radioactive decay inside the planet and primordial heat left over from the planet's formation. It's a tiny amount compared to the energy the Earth used to receive from the Sun, but it builds up over time. In the end, you'll have a scorching hot cave with maybe a few extremophile strains of bacteria left.

Answer 2

Cooked Earth (eventually)

In the short term(1 year): Darkness descends on the whole earth. No sunlight, no photosynthesis. All plants die, which promptly leads to all animal life starving. Or possibly choking to death on all the released CO2 and methane from decomposition of a couple trillion tons of dead plants.
The Sphere prevents heat loss by perfectly mirroring, so the Earth quite rapidly (on scale of a few weeks at most) attains a uniform surface temperature. This is very cold for the equator but very very warm for the polar regions. Every single speck of ice on Earth melts. The entire surface stabilizes at about 10 Celcius. his is colder than the current average surface temperature, because all that ice melting will absorb a tremendous amount of energy. But melt it will, as the sky above it "shines" with the mirrored surface heat of the whole Earth.

Climate? Expect some interesting floods, including swamped shorelines, due to all the melting ice. There will be no energy input into ocean evaporation and air convection, so the rains will almost immediately stop. Winds will rapidly drop down to very vague breezes only, caused by the slowly equalizing temperatures around them. With no differential hot and cold spots, the weather will essentially just cease to exist.

In the Medium long term(about 100 000 years):
The Earth then proceeds to cook itself.
With no cooling factor on the surface, with the core still at about 5000 Celcius, the whole Earth will eventually attain a uniform temperature. Something like 4500C.

In the really, really long term (several billion years):
The Earth still contains a lot of radioactive isotopes, that still undergo normal radioactive decay, with the energy release that goes with that.
End result: Earth will settle at between 45000 and 50000K, once all radioactives have decayed. This will take a while, make sure you have taken out the extended warranty on the Universe, with optional "outside interference" clauses. Can't have the sun going red giant interfere with our little cooking experiment, can we?