By now, you have learned to model complex thermal systems, and would like to apply your newfound skills to model our beautiful planet. You are tasked to estimate how sensitive our planet's surface temperature is to greenhouse gas emissions. As a human, you are mainly concerned with the planet's temperature within 5m of the surface. The surface is sandwiched between the atmosphere and the heated core. Thermal radiation from the sun strikes the Earth's surface at solar = 1000 , and approximately 30% is reflected back out to space and 70% is absorbed by Earth's surface. You are interested in knowing how sensitive the Earth's surface temperature is to changes in percentage of solar radiation being reflected. Consider the first 5 m beneath the surface as our control volume, shown in dash lines, and
a) perform a general energy balance of the surface considering unsteady effects. You may assume the surface to have uniform temperature. You should consider effects from Earth's core, atmospheric flow, thermal radiation, etc.
b) Identify each term and provide numerical values. Determine and justify any assumptions, for instance, material properties.
c) Based on your assumptions, what is the average surface temperature of the Earth? Is this reasonable? If not, you should try a different approach and/or revisit your assumptions.
d) If the percentage of thermal radiation absorbed by the surface suddenly increases to 80% due to greenhouse gas emissions, what would the surface temperature be?
e) How long would this surface temperature increase take?