Second Law Analysis of the Earth System with a Radiative Model

Abstract

Solar radiation provides the energy for many processes on Earth including processes that sustain living systems and circulation of the atmosphere and oceans. The Earth does not consume this energy; it is simply converted to outgoing thermal radiation. However, the entropy production rate of Earth causes energy degradation and the exergy destruction rate quantifies this degradation relative to a reference environment. The global entropy production rate also provides an additional constraint for comparison with atmospheric modeling results. In this paper a simplified expression for the global entropy production rate, associated with the absorbed portion of the solar flux, is presented based on a radiative model. The second purpose of this work is to investigate the exergetic analysis of the Earth. It is desirable to consider environment temperatures that are typical temperatures on Earth when comparing the total entropy production rate and irreversibility rate of the planet to those due to processes such as the global energy system; in other words, typical temperatures where these processes occur. However, multiplying the estimated global entropy production rate by an arbitrary environment temperature appears to result in irreversibility rates that violate the second law of thermodynamics. It is shown that the radiative interaction of the Earth with its surroundings can be theoretically modeled and tested in a laboratory environment showing that arbitrary environment temperature specifications should not cause these violations. These apparent violations are resolved through corrections to the energy, entropy and exergy calculations that are due to the specific character of radiative heat transfer. As a result, this analysis also provides an illustrative example of the implications of environment specifications on exergy analysis involving radiative heat transfer.

Keywords

• reversible thermodynamics, irreversibility, entropy production, exergy analysis, atmospheric modeling, radiative planetary model