A solar pond is built to test the possibility of generating power. The maximum thermal efficiency and the maximum power generation need to be determined.


A Heat Engine can Work between a Solar Pond and the Ambient Air


(1) Determine the maximum thermal efficiency

Assuming the power plant is a Carnot heat engine, which works between a source at temperature 85 oC, and a sink at temperature 35 oC.

      ηth,rev = 1 - (35+273)/(85+273) = 14%

(2) Determine the maximum power generated by the pond

The definition of the thermal efficiency of a heat engine is

      ηth = Wnet,out/Qin

Rearranging this equation gives

      Wnet,out = Qin ηth

If the efficiency of this heat engine equals the Carnot efficiency, and the heat absorbed by the salt water is totally input to the heat engine, the output net work can achieve its maximum value.

      Wnet,max = QHηth,rev

The bottom area of the pond is

      Apond = (10) (10) = 100 m2

Heat absorbed by the salt water in the pond bottom area is

      QH = (0.3) (100) = 30 kW

Hence, the maximum net work output by the heat engine equals

      Wnet,out,max = Qin ηth,rev = ( 30)(0.14) = 4.2 kW