Question

Part C: The Earth’s atmosphere can be considered to be a heat engine, in the Carrot (thermodynamic) sense. The temperature at top of the upper atmosphere is that necessary to radiate infrared energy back into space so to balance that gained from the sun. The surface is heated by the sun and insulated by the atmosphere (the greenhouse effect) so it’s warmer.

1) What is the efficiency of this heat engine if the air at Earth’s surface is 288 K (15°C) and the upper atmosphere gas that is radiating energy to space is at 255 K (-18°C)?

2) The average amount of the Sun’s energy per second that is available to heat the air near the surface
is 240 W/m2 (Note 1). How much work per second does the atmosphere do, per square meter? (Note 2)

3) What does this work do?

4) Repeat your calculations in 1) and 2) if the surface warms by 2°, and comment on what it may do to your answer in 3).

Note 1: the solar constant is 1000 W/m2 at the surface, but half the Earth is in shadow, and most of the rest of the surface isn’t pointed square to the Sun.
Note 2: The Earth has a surface area of about 510 trillion square meters (5.1x1014 m2; 510 million km2), so globally this is an immense amount of energy.

Answer 1

In this solution some basic concepts and formulas of Thermodynamics are used. For more information, refer to any standard textbook or drop a comment below. Please give a positive rating if solution is helpful.