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- Thread starter higheye
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Once the power station ia ready, calculate its thrmodynamic efficiency, assuming cooling towers maintain a temperatue of 70 degrees C and hence the amount of electrical energy (in J) from one mole of methane.

Thats the question as it is on paper.

The whole sheet is on a power station starting up from cold. Initally the boiler contains 23,000 kg of water at a temp of 10 degree C.

I was then asked to calculate the energy need to raise water to boiling point

The energy required to vaporise all water to steam

Energy required to raise temp of steam to 500 degrees C

It told me to add these 3 results then, (from which I got 119 GJ), and stated this is the power stations (rough estimate) amount of energy needed to prepare it for electrical generation.

My next question is to calculate the mass of methane that must be burnt to prepare the power station for generation. I calculated this, and now on the 5th question that I wrote at the begining.

Data I been given: Molar heat capacity of water - 75.29 J K-1 Mol-1

'' '' '' steam - 36.54 J K-1 Mol-1

Enthalpy of Vapourisation of water - 40.656 kJ Mol-1

Enthalpy of combustion if methane - -890 kJ Mol-1

Gibbs free energy for the combustion of methane - -845 kJ Mol-1

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am i right in calculating the work done is the energy used to transfer 890 kJ from the methane, heating up the water to boiling then vapourising then heating steam to 500 C?

Is the above equation the same as: 1 - (the absolute temperature of cold resevoir/the absolute temperature of hot resevoir)

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efficiency = work done by system / energy put in

am i right in calculating the work done is the energy used to transfer 890 kJ from the methane, heating up the water to boiling then vapourising then heating steam to 500 C?

No, this is the work done by the heat engine, resulting from the heat it consumes. In your case the work done is spinning the generator's shaft. You can't calculate this directly, rather, you compute the efficiency in some other way and since you know the input heat, you can then estimate the work done.

Is the above equation the same as: 1 - (the absolute temperature of cold resevoir/the absolute temperature of hot resevoir)

In the case of the Carnot cycle, yes. Note that a real power plant does not use the Carnot cycle, the Carnot cycle is only the the upper bound theoretical estimate.

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then I can re-arrange the the top one: work done = 0.86 * 890 kJ?

this come out to work done = 765.4 kJ

Is this sensible? i really dont know?

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ah so i can take the second equation like this: 1 - ( 70 / 500 ) = 0.86

You need to use the absolute temperature.

then I can re-arrange the the top one: work done = 0.86 * 890 kJ?

this come out to work done = 765.4 kJ

Yes, that's the principle (but the numbers are wrong). Note that what you get is mechanical energy. There is also some loss of energy when it is converted to electrical energy, but the loss is negligible. I leave it to you to find out the efficiency of power plant electrical generators to prove that.

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I re-calculated the mechanical energy and resulted in 356 kJ

This seems incorrect. Please show your calculations.

I have been researching and to no avail have I been able to progress with working out how much electrical energy is produced. Maybe im looking for the wrong thing? I been looking for equations or conversions for mechanical enrergy into electrical energy through generators. Am i at least on the right path? Maybe I need sleep

You merely need to find some facts on the current electrical generators. For example: http://www.energy.siemens.com/hq/en/power-generation/generators/sgen-4000w.htm

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1 - ( 343.15 / 773.15 )

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This result seems correct.

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why has it given me the 1 mole information and electrical energy information?

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