Question

An engincer designs a ship that gets its power in the following way: The engine draws in warm water from the ocean, and after extracting some of the water's internal energy, returns the water to the ocean at a temperature \(14.5^{\circ} \mathrm{C}\) lower than the ocean temperature. If the ocean is at a uniform temperature of \(17^{\circ} \mathrm{C},\) is this an efficient engine? Will the engineer's design work?

Short answer

Explain your reasoning. The design of the ship's engine is not efficient and is unlikely to work well because the maximum possible efficiency, calculated using the Carnot Efficiency formula, is only 5%. This low efficiency is not sufficient for practical applications, indicating that the engineer should explore other designs and concepts for the ship's engine.

Step-by-step solution

State the Given Information

The engine draws in warm water from the ocean at a temperature of \(17^{\circ}\mathrm{C}\). The engine returns the water at a temperature of \(14.5^{\circ}\mathrm{C}\) lower than the ocean temperature.

Convert Temperatures to Kelvin

We'll need to convert the given temperatures in Celsius to Kelvin, as it's necessary for thermodynamic calculations. The conversion formula is: \(K = C + 273.15.\) Ocean temperature (in Kelvin): \(17^{\circ}\mathrm{C} + 273.15 = 290.15 K\) Returned water temperature (in Kelvin): \((17 - 14.5)^{\circ}\mathrm{C} + 273.15 = 275.65 K\)

Calculate Efficiency using Carnot Efficiency

Since it is a heat engine, we will calculate the maximum possible efficiency using the Carnot Efficiency formula: Carnot Efficiency = \(1 - \frac{T_C}{T_H}\) Where \(T_H\) is the temperature of the hot reservoir (ocean) and \(T_C\) is the temperature of the cold reservoir (returned water). Carnot Efficiency = \(1 - \frac{275.65}{290.15} = 1 - 0.9500 = 0.0500\) The maximum possible efficiency of this engine is \(5\%\).

Evaluate the Efficiency and Design

A \(5\%\) efficiency is very low for an engine. Therefore, from the perspective of efficiency, this engine design is not efficient and would not work well. In conclusion, the engineer's design of a ship's engine that extracts energy from the temperature difference in water is not efficient and most likely will not work well. The low efficiency of \(5\%\) is not sufficient for practical applications, and the engineer should explore other designs and concepts for the ship's engine.