Um inventor sugeriu a construção de uma central térmica, visando a aproveitar a diferença de temperatura existente entre a água situada próxima à superfície do oceano e a água situada em profundidades mais elevadas, onde as temperaturas são bastante baixas. Essa central irá absorver o calor da água quente próxima à superfície e rejeitar calor da água fria a algumas centenas de metros de profundidade. Sabendo-se que as temperaturas envolvidas nas duas regiões mencionadas valem, respectivamente, 25 °C e 5 °C, o rendimento térmico máximo dessa central, em %, será, aproximadamente,

The correct answer is B) 6.7. To understand why, let's dive into the concept of thermoelectric power plants.

The inventor's idea is to harness the temperature difference between the warm water near the ocean's surface and the cold water at greater depths. This temperature difference can be used to generate electricity. The plant would absorb heat from the warm water and reject heat to the cold water, creating a thermodynamic cycle.

The efficiency of a thermoelectric power plant is limited by the Carnot cycle, which is the maximum possible efficiency of a heat engine. The Carnot efficiency is given by the formula:

$$eta = 1 - frac{T_c}{T_h}$$

where $eta$ is the efficiency, $T_c$ is the temperature of the cold reservoir (in Kelvin), and $T_h$ is the temperature of the hot reservoir (in Kelvin).

In our case, the hot reservoir is the warm water near the ocean's surface, with a temperature of 25°C (298 K), and the cold reservoir is the cold water at greater depths, with a temperature of 5°C (278 K). Plugging these values into the formula, we get:

$$eta = 1 - frac{278}{298} = 0.067$$

Therefore, the maximum thermoelectric efficiency of the plant is approximately 6.7%, which corresponds to answer B) 6.7.

It's worth noting that this is an idealized calculation, and the actual efficiency of the plant would be lower due to various losses and imperfections. However, this calculation gives us an estimate of the maximum possible efficiency of the plant.