Thermodynamics energy efficiency

[donkey11]

Homework Statement

Each second, a nuclear power plant generates 2000 MJ of thermal energy from nuclear reactions in the reactors core. This energy is used to boil water and produce high pressure steam at 573 Kelvins, the steam spins a turbine, which produces 700 MJ of electric power, then the steam is condensed and water is cooled to 303 kelvins before starting cycle again.
a) maximum possible efficiency of plant?
b) plant's actual efficiancy?

Homework Equations

emax= 1 - (Tc/Th)
e= what you get/ what you pay

The Attempt at a Solution

a)emax= 1- (303/573) = 0.53
b) e= work out/Qh = Qh-Qc/Qh = 1300/2000 = 0.65
but this is larger then my max!

 

[learningphysics]

Shouldn't the plant's efficiency be: 700/2000 ?

The electric power produced is 700MJ. That's what you get. What you pay is 2000 MJ.

 

[ogb p]

I would like to clarify a few things about the efficiency of a power plant. First, the maximum possible efficiency of any power plant is determined by the laws of thermodynamics and is known as the Carnot efficiency, which is given by the equation emax= 1 - (Tc/Th), where Tc is the temperature of the cold reservoir (in this case, 303 K) and Th is the temperature of the hot reservoir (573 K). This means that the maximum possible efficiency of the power plant in this scenario is 1- (303/573) = 0.47 or 47%.

Secondly, the actual efficiency of a power plant is typically lower than the maximum possible efficiency due to various factors such as energy losses, heat transfer inefficiencies, and mechanical losses. In this case, the plant's actual efficiency can be calculated by using the equation e= work out/Qh, where work out is the work output (700 MJ) and Qh is the heat input (2000 MJ). This gives an efficiency of 700/2000 = 0.35 or 35%.

It is important to note that the actual efficiency of a power plant can vary depending on several factors such as the design, maintenance, and operating conditions. Therefore, it is crucial to continuously monitor and improve the efficiency of power plants to ensure maximum energy efficiency and minimize energy wastage.