An ocean thermal gradient electric generating system is proposed for siting in Salalah. This system would operate a heat engine driven by heat flow from warm ocean water (cooled from 27 ⁰C to 25 ⁰C in the heating heat exchanger of the system), and cooled by heat flow to cold ocean water (which is heated from 3 ⁰C to 5 ⁰C in the cooling heat exchanger of the system). The ocean water used in the different parts of the heat engine is obtained from different depths of the surrounding sea. Using this heat engine electricity can be produced at 90% of the corresponding Carnot efficiency of the heat engine and heat capacity of water is 4.2 kJ/(kg.K). (i) What is the value of the Carnot efficiency of the heat engine? Explain the basis for selecting the parameter values used in calculating this value. [(ii) Should the cold ocean water flow through the engine at a rate of 100 million kg/min, what is the electric power output of the engine. (iii) What is the corresponding flow rate of warm ocean water? (iv) Friction losses arising in pumping seawater through the engine account for 0.33 of the engine’s irreversibility (maximum work-electrical power). What would be the resulting value of the heat engine’s efficiency? (v) Discus and justify your results.
An ocean thermal gradient electric generating system is proposed for siting in Salalah. This system would operate a heat engine driven by heat flow from warm ocean water (cooled from 27 ⁰C to 25 ⁰C in the heating heat exchanger of the system), and cooled by heat flow to cold ocean water (which is heated from 3 ⁰C to 5 ⁰C in the cooling heat exchanger of the system). The ocean water used in the different parts of the heat engine is obtained from different depths of the surrounding sea. Using this heat engine electricity can be produced at 90% of the corresponding Carnot efficiency of the heat engine and heat capacity of water is 4.2 kJ/(kg.K).
(i) What is the value of the Carnot efficiency of the heat engine? Explain the basis for selecting the parameter values used in calculating this value. [
(ii) Should the cold ocean water flow through the engine at a rate of 100 million kg/min, what is the electric power output of the engine.
(iii) What is the corresponding flow rate of warm ocean water?
(iv) Friction losses arising in pumping seawater through the engine account for 0.33 of the engine’s irreversibility (maximum work-electrical power). What would be the resulting value of the heat engine’s efficiency?
(v) Discus and justify your results.
A Carnot engine is a simplified engine that employs reversible mechanical and thermal interactions. This means the engine can go through its motions and return to its original condition without increasing entropy (without energy loss). The engine must be in thermal equilibrium throughout its cycle in order to return to its initial condition without increasing entropy.
Carnot pondered the concept of maximum efficiency in a heat engine, wondering if the efficiency of a heat engine could approach 100%, or if there was a limit that could not be exceeded
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