Power & Engine efficiency - Using heat (kelvin)

TJ and PJ stand for Terrajoules and Petajoules respectively.In summary, the conversation discusses a power plant that uses geothermal energy to produce electricity. The maximum efficiency of the plant is calculated using the Carnot cycle. The minimum amount of rejected heat that must be removed from the condenser every 24 hours is also calculated. The output power of the generator is 84 MW. The units TJ and PJ stand for Terrajoules and Petajoules, respectively.
  • #1
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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  • #2
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
 

1. What is the relationship between power and engine efficiency?

The relationship between power and engine efficiency is that as the power output of an engine increases, the efficiency decreases. This is because more energy is being used to produce power, resulting in less energy being converted into useful work. However, with advancements in technology, engines are becoming more efficient while still maintaining high power outputs.

2. How does heat affect engine efficiency?

Heat plays a crucial role in engine efficiency. In the Carnot heat engine cycle, the efficiency of an engine is directly proportional to the difference in temperature between the hot and cold reservoirs. This means that the higher the temperature difference, the more efficient the engine will be. However, excessive heat can also lead to engine damage and decreased efficiency.

3. What is the Kelvin scale and why is it used to measure heat in relation to engines?

The Kelvin scale is an absolute temperature scale where 0 Kelvin represents absolute zero, the theoretical temperature at which all molecular motion stops. This scale is used in relation to engines because it allows for more accurate measurements of heat, as it does not have negative values like the Celsius and Fahrenheit scales do.

4. Can engine efficiency be improved by using heat from external sources?

Yes, external heat sources such as waste heat from industrial processes or solar energy can be used to improve engine efficiency. This is known as waste heat recovery or heat-to-power systems, where the excess heat is converted into useful energy to increase the overall efficiency of the engine.

5. How do scientists and engineers work to increase engine efficiency using heat?

Scientists and engineers work to increase engine efficiency using heat through various methods such as improving engine design, utilizing waste heat recovery systems, and developing new technologies such as hybrid and electric engines. They also conduct research to understand the thermodynamics and properties of different fuels to optimize their use in engines for increased efficiency.

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