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.

      η_th,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

      η_th = W_net,out/Q_in

Rearranging this equation gives

      W_net,out = Q_in η_th

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.

      W_net,max = Q_Hη_th,rev

The bottom area of the pond is

      A_pond = (10) (10) = 100 m²

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

      Q_H = (0.3) (100) = 30 kW

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

      W_net,out,max = Q_in η_th,rev = ( 30)(0.14) = 4.2 kW