Assertion (A) Analysis: OTEC Power Plant Efficiency

Ocean Thermal Energy Conversion (OTEC) power plants utilize the temperature difference between warm surface ocean water and cold deep ocean water to generate electricity. This temperature difference is typically small, often around 20°C. Due to this limited temperature gradient, the maximum theoretical efficiency achievable is inherently low. Therefore, Assertion (A) stating that OTEC power plants have low efficiencies is correct.

Reason (R) Analysis: Thermodynamics Governing Efficiency

The second law of thermodynamics places fundamental limits on the efficiency of any heat engine. According to the Carnot theorem, the maximum possible efficiency ($\eta_{Carnot}$) for a heat engine operating between a hot reservoir at temperature $T_H$ and a cold reservoir at temperature $T_C$ is given by:

$ \eta_{Carnot} = 1 - \frac{T_C}{T_H} $

Where $T_C$ and $T_H$ are absolute temperatures (in Kelvin). Real-world heat engines always operate at efficiencies lower than the Carnot limit due to various irreversibilities. Thus, Reason (R) stating that efficiency is governed by the 2nd law of thermodynamics is correct.

Explanation Linking Assertion and Reason

OTEC plants function as heat engines. The low efficiency of OTEC plants (Assertion A) is a direct consequence of the small temperature difference ($T_H - T_C$) available in the ocean environment. This small temperature difference significantly limits the Carnot efficiency, as dictated by the second law of thermodynamics (Reason R). Therefore, the second law of thermodynamics provides the fundamental reason for the low efficiencies observed in OTEC power plants.

Conclusion

Both Assertion (A) and Reason (R) are true statements. Furthermore, Reason (R) correctly explains the underlying scientific principle (governed by the 2nd law of thermodynamics) that leads to the low efficiencies stated in Assertion (A).

The correct option is: Both (A) and (R) are correct and (R) is the correct explanation of (A).