Power & Engine efficiency - Using heat (kelvin)

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SUMMARY

The discussion focuses on calculating the maximum efficiency and heat rejection of a geothermal power plant operating at 505 K and condensing at 323 K. The maximum efficiency can be determined using the Carnot efficiency formula: 1 - (Tc/Th), where Tc is the cold reservoir temperature and Th is the hot reservoir temperature. The output power of the generator is 84 MW, which is essential for calculating the minimum amount of rejected heat over 24 hours. The discussion also clarifies that TJ and PJ refer to Terrajoules and Petajoules, respectively.

PREREQUISITES
  • Understanding of Carnot efficiency and thermodynamic cycles
  • Familiarity with geothermal energy systems
  • Knowledge of power calculations in megawatts (MW)
  • Basic concepts of heat transfer and energy units (MJ, TJ, PJ)
NEXT STEPS
  • Study the Carnot efficiency formula in detail
  • Learn about geothermal energy conversion processes
  • Research methods for calculating heat rejection in thermal systems
  • Explore energy unit conversions, specifically between MJ, TJ, and PJ
USEFUL FOR

Engineers, thermodynamics students, and professionals in the renewable energy sector seeking to understand the efficiency and energy dynamics of geothermal power plants.

MikeNZ
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Homework Statement



1. Homework Statement
A power plant taps steam superheated by geothermal energy to 505 K (the temperature of the hot reservoir) and uses the steam to do the work in turning the turbine of an electric generator. The steam is then converted back into water in a condenser at 323 K (the temperature of the cold reservoir), after which the water is pumped back down into the ground where it is heated again. The output power of the generator is 84 MW. Calculate:

1) The maximum efficiency at which this plant can operate
2) The minimum amount of rejected heat (in MJ) that must be removed from the condenser every 24 hours
3) Express your answer to (2) in TJ and in PJ.

(Quick question - what would TJ and PJ mean? Terrajoules and Petajoules or something?


Homework Equations





The Attempt at a Solution



For (1) - Can I calculate the ratio of heat going in, to heat going out.. and then use that ratio to the 84 MW to get the maximum efficiency?

I'm thinking for number (2) - Since 84 MW is power - meaning there's a time.. you can calculate the energy (without the time) and then apply that over the 24 hours (still trying to find the right equation) - I'm really stuck on number 2.

Number (3) - Have no idea as we have not been taught that - If it is Terrajoules and Petajoules, then it must be a simple case of moving the decimal point.
 
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For 1- All you have to do is find the ideal efficiency, which is the same as the carnot cycle calculation:

1-(Tc/Th)

for 2- Yeah that would work
for 3- Yup
 

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