Atmospheric chemistry and the biosphere: general discussion

The most common elements in organic molecules, carbon, hydrogen, oxygen, nitrogen, sulfur, and phosphorus, are only available in the ecosystem in limited amounts. Therefore, these nutrients must be recycled through both biotic and abiotic components of the ecosystem, in processes generally called biogeochemical cycles.

Sulfur, an important element in the chemical makeup of proteins, is recycled through the atmosphere and aquatic and terrestrial environments. Found in the atmosphere as sulfur dioxide (SO2), sulfur is released by decaying organisms, weathered rocks, geothermal vents, volcanos, and burning fossil fuels. It is deposited into the ecosystem, cycled through the biotic community, and either released back into the atmosphere as gas or deposited in marine sediment for long-term storage and eventual...

Climate refers to the prevailing weather conditions in a specific area over an extended period. As the saying goes, “Climate is what you expect. Weather is what you get.” Climate is influenced by geographic factors, such as latitude, terrain, and proximity to bodies of water.

Around 4 billion years ago, oceans began to condense on earth while volcanic eruptions released nitrogen, carbon dioxide, methane, ammonia, and hydrogen into the primordial atmosphere. However, organisms with the characteristics of life were not initially present on earth. Scientists have used experimentation to determine how organisms evolved that could grow, reproduce, and maintain an internal environment.

Change in atmospheric pressure with height is particularly interesting. The decrease in atmospheric pressure with increasing altitude is due to the decreasing gravitational force per unit area as we move away from the surface of the earth.
Assuming the air temperature is constant at a given altitude and that the ideal gas law of thermodynamics describes the atmosphere to a good approximation, one can find the variation of atmospheric pressure with height.
Let p(y) be the atmospheric pressure at...

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