Question

Calvin Cliffs Nuclear Power Plant, located on the Hobbes River, generates 1.00 GW of power. In this plant, liquid sodium circulates between the reactor core and a heat exchanger located in the superheated steam that drives the turbine. Heat is absorbed by the liquid sodium in the core, and released by the liquid sodium (and into the superheated steam) in the heat exchanger. The temperature of the superheated steam is 458 K. Heat is released into the river, and the water in the river flows by at a temperature of 28°C. 1) (a) What is the highest efficiency that this plant can have? Recall that the highest efficiency of any engine is given by the Carnot efficiency.

Answer 1

Answer:

The highest efficiency is 34.28%

Solution:

As per the question:

Power generated, P = 1 GW = $1\times 10^{9} W$

Temperature of the super heated steam, T = 458 K

Temperature of the water flowing in the river, T' = $28^{\circ}C$ = 301 K

Now,

(a) The efficiency can be given by utilizing the Carnot efficiency:

$\eta_{C} = 1 - \frac{T'}{T} = 1 - \frac{301}{458} = 1 - 0.6572 = 0.3428$

%$\eta = 0.3428\times 100 = 34.28$%