Question

Note that you will most likely get different numbers for the different parts below. As usual, a good way to handle that is to solve the problem using variables, and only plug in numbers at the end.

A solar pond is a pond full of saltwater that acts as a solar energy collector. A key feature of the pond is a salt concentration gradient in the water, with a higher concentration of salt at the bottom. The energy in sunlight entering the pond is absorbed mostly at the bottom, raising the temperature of the bottom of the pond up to around 90°C. In fresh water, the warm water would be less dense and rise to the top, but in the solar pond the larger salt concentration at the bottom ensures that the water at the bottom is always more dense than the water above it, so the higher temperature water remains at the bottom of the pond.

Let's say that the temperature at the bottom of the pond is 86.0 °C and the temperature at the top of the pond is 29.0 °C .

Given these two temperatures, what is the maximum possible efficiency a heat engine based on the salt pond can have? Note that such a salt pond is used in El Paso, Texas, to supply one-fifth of the energy requirements of the Bruce Foods Corporation.
_______ %

Part (b)

Let's say that the temperature at the bottom of the pond is 86.0 °C and the temperature at the top of the pond is 29.0 °C . In addition, 7500 J of useful energy (we call this work) is supplied by the heat engine. Assuming this is done at maximum possible efficiency, how much energy was extracted by the heat engine from the higher-temperature water?
_______ J

Answer 1