- efficiency heat engine carnot
*assignment*Power from the Ocean*assignment*Homework##### Power from the Ocean

heat engine efficiency Energy and Entropy Fall 2020 Energy and Entropy Fall 2021It has been proposed to use the thermal gradient of the ocean to drive a heat engine. Suppose that at a certain location the water temperature is \(22^\circ\)C at the ocean surface and \(4^{o}\)C at the ocean floor.

What is the maximum possible efficiency of an engine operating between these two temperatures?

- If the engine is to produce 1 GW of electrical power, what minimum volume of water must be processed every second? Note that the specific heat capacity of water \(c_p = 4.2\) Jg\(^{-1}\)K\(^{-1}\) and the density of water is 1 g cm\(^{-3}\), and both are roughly constant over this temperature range.

*group*Heat and Temperature of Water Vapor (Remote)*group*Small Group Activity5 min.

##### Heat and Temperature of Water Vapor (Remote)

In this introduction to heat capacity, students determine a derivative that indicates how much the internal energy changes as the temperature changes when volume is held constant.-
Energy and Entropy Fall 2020
Energy and Entropy Fall 2021
At a power plant that produces 1 GW (\(10^{9} \text{watts}\)) of electricity, the steam turbines take in steam at a temperature of \(500^{o}C\), and the waste energy is expelled into the environment at \(20^{o}C\).

What is the maximum possible efficiency of this plant?

Suppose you arrange the power plant to expel its waste energy into a chilly mountain river at \(15^oC\). Roughly how much money can you make in a year by installing your improved hardware, if you sell the additional electricity for 10 cents per kilowatt-hour?

At what rate will the plant expel waste energy into this river?

Assume the river's flow rate is 100 m\(^{3}/\)s. By how much will the temperature of the river increase?

- To avoid this “thermal pollution” of the river the plant could instead be cooled by evaporation of river water. This is more expensive, but it is environmentally preferable. At what rate must the water evaporate? What fraction of the river must be evaporated?