Thermodynamic Efficiency of Brittle Frictional Mountain Building

An active fold-and-thrust belt in unchanging tectonic and climatic conditions attains a dynamic steady-state in which the influx of accreted material at the toe is balanced by the erosive efflux off the top. The overall balance of energy in such a steady-state fold-and-thrust belt is described by the equation $\dot{E}=\dot{W}_{\text{G}}+Q$, where $\dot{E}$ is the rate at which both mechanical and heat energy are added from external sources, $\dot{W}_{\text{G}}$ is the rate of work performed against gravitational body forces, and Q is the rate at which waste heat flows out of the upper and lower boundaries. The total amount of power being supplied to the active Taiwan fold-and-thrust belt by the subducting Eurasian plate and in situ radioactivity is 4.2 gigawatts. Because only 0.5 gigawatts are expended in doing useful work against gravity and the remaining 3.7 gigawatts are ejected as heat, the efficiency of brittle frictional mountain building in Taiwan is 11 percent.