Maximum possible efficiency of a coal-burning power plant
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Maximum possible efficiency of a coal-burning power plant

[From: ] [author: ] [Date: 11-04-25] [Hit: ]
http://en.wikipedia.Tc is the cold temperature and Th the hot temperature. Both need to be in Kelvin.0 K = − 273.1 - 303.......
A coal-burning power plant produces 3000 MW of thermal energy, which is used to boil water and produce supersaturated steam at 300 degrees Celsius. This high-pressure steam turns a turbine producing 1000 MW of electrical power. At the end of the process, the steam is cooled to 30 degrees Celsius and recycled.
What is the maximum possible efficiency of the plant?
What is the actual efficiency of the plant?
To cool the steam, river water runs through a condenser at a rate of 40x10^6 gal/h. If the water enters the condenser at 20 degrees Celsius, what is its exit temperature?

I'm so lost, i don't know where to start!

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The maximum possible efficiency can be calculated using Carnot's theorem.
http://en.wikipedia.org/wiki/Thermal_eff…

1-Tc/Th
Tc is the cold temperature and Th the hot temperature. Both need to be in Kelvin.

0 K = − 273.15 C
1 - 303.15k/573.15K=0.471
So the maximum efficiency is 47.1 %
The actual efficiency is 100/3000MW * 1000MW = 33.3%

The heat capacity of water is 4.18 kJ/(kg*K)
40*10^6 gal = 3.785 * 40 * 10^6 kg = 151.4 * 10^6 kg
The waste heat is 2000MW, that means 2000MWh per hour.
2000MWh = 2000MWh * 3600 s/h = 7,200,000 MWs = 7,200,000 MJ = 7.2 * 10^9 kJ

7.2 * 10^9 kJ / (151.4 * 10^6 kg * 4.18 kJ/(kg*K)) = 11.38 K
20 C + 11.38 K = 31.38 C
1
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