How Efficient Is a Steam-Electric Power Plant That Delivers 900 MW?

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SUMMARY

The efficiency of a steam-electric power plant delivering 900 MW of electric power is calculated to be approximately 25%. This conclusion is derived from the heat loss through cooling water, which has a mass flow rate of 629,000 kg/s and a temperature increase of 1.03 °C. The calculations involve using the specific heat capacity of water (4184 J/kg·K) to determine the total heat loss, allowing for an accurate efficiency assessment. The initial miscalculation of 19% was corrected by factoring in the specific heat and total output of the plant.

PREREQUISITES
  • Understanding of thermodynamic efficiency calculations
  • Knowledge of specific heat capacity, particularly for water (4184 J/kg·K)
  • Familiarity with power units, specifically megawatts (MW) and joules per second (J/s)
  • Basic principles of heat transfer and energy conservation
NEXT STEPS
  • Study thermodynamic efficiency formulas, specifically Efficiency = W/Qh
  • Learn about heat transfer principles in power plants
  • Explore the impact of cooling systems on power plant efficiency
  • Investigate advanced calculations for thermal efficiency in steam-electric plants
USEFUL FOR

Engineering students, energy analysts, and professionals involved in power generation and thermal efficiency optimization will benefit from this discussion.

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Homework Statement



(c13p30) A steam-electric power plant delivers 900 MW of electric power. The surplus heat is exhausted into a river with a flow of 6.29×10^5 kg/s, causing a change in temperature of 1.03 oC. What is the efficiency of the power plant (in % Don't enter a unit.)?

Homework Equations



Not sure with this one. Efficiency = 1 - Tc/Th, or Efficiency = W/Qh

The Attempt at a Solution



900MW = 900,000,000 J/s

900,000,000 J/s / 629,000 kg/s = 1430.8

1.03 Deg C = 274.18 K

274.18 K / 1430.8 = .19

So 19%
 
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As I read the problem text, cooling water leaves the plant with the given mass flow rate and with the given temperature increase. Knowing the heat capacity of water you should be able to calculate how much power is lost via the cooling water, so the efficiency must be how much 900 MW are relative to the total output of the plant (900 MW + loss). Doing that calculation you should get around 25%.
 
That was the answer, thanks :-)

Also after seeing what you said I figured out how to do it

I was factoring in the specific heat (4184) or using my formulas correctly.

Thanks for your help !
 

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