A typical coal-fired power plant burns 250 metric tons of coal every hour to gen

Question

A typical coal-fired power plant burns 250 metric tons of coalevery hour to generate 2.8×106 MJ of electricity. 1 metric ton= 1000 kg; 1 metric ton of coal has a volume of 1.5 m3.The heat of combustion is 28 MJ/kg. Assume that allheat is transferred from the fuel to the boiler and that all the work done in spinning the turbine is transformed into electrical energy.

Part A

Suppose the coal is piled up in a 12 m × 15 m room. How tall must the pile be to operate the plant for one day?

Part B

What is the power plant's thermal efficiency?

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Smaller mammals use proportionately more energy than larger mammals; that is, it takes more energy per gram to power a mouse than a human. A typical mouse has a mass of 20 g and, at rest, needs to consume 3.0 Cal each day for basic body processes.

How much greater is this than the resting power noted in the chapter (100 W)?

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A newly proposed device for generating electricity from the sun is a heat engine in which the hot reservoir is created by focusing sunlight on a small spot on one side of the engine. The cold reservoir is ambient air at 20 C. The designer claims that the efficiency will be 60%.

What minimum hot-reservoir temperature, in C, would be required to produce this efficiency?

Explanation / Answer

- The plant burns 250 tons per hour to produce 2.8 e6 MJ (each hour)
- 1 ton = 1000 kg
- The Volume of 1 ton is 1.5 m^3
- Heat of combustion (the energy you get from burning per kg) 28 MJ/kg

(a) The question is only asking how much space would the coal required for one day of plant operation occupy? First, note that the plant uses 250 tons per hour * 24 hours per day coal each day. The volume of 1 ton of coal is 1.5 m^3. So, the volume of coal used in a day is 1.5 * 24*250 = 9000 m^3. If we put this into a pile of dimension 10 x 10 x h meters, we have that 10*10*h = 9000 m^3, so h = 90 m.

(b) Efficiency, briefly is energy output/energy input. For this plant, the question is how much of the available chemical energy of the coal is converted to electricity? We know that the plant outputs 2.8e6 MJ of electricity each hour, so how much chemical energy is input?

Note that the plant uses 250 tons of coal per hour. There are 1000 kg in a ton. Each kg, when burned, gives 28 MJ of energy. All we do now is multiply:

250 tons * 1000 kg/ton * 28 MJ/kg = 7000,000 MJ = 7e6 MJ.

So input = 7 e6 MJ, output = 2.8e6 MJ. The efficiency is a fraction equal to the output/input, which is:

2.8e6/7e6 = 27/84 = 0.4

So the plant is 40% efficient. That is, for each 1 part of input energy, only 0.40 part of that is converted to electrical energy. The rest - 60% is lost as heat (mostly).

2) mouse nees 3.0 Cal / 20 g = 0.15 Cal/g

if human needs the same amount of energy per g, then that is
68 kg * 3.0 Cal / 20g = 68000 g * 3.0 Cal / 20 = 3400 * 3 Cal = 10200 Cal

10200 Cal/day which is about 5 times the 2000 Cal per day that is recommended.

3) Let T = minimum temperature in degree K of the hot reservoir needed
Ambient air temperature = 20 + 273 = 293 K
By Carnot's theorem, maximum efficiency (as a fraction) = (T - 293) / T
=> (T - 293) / T = 60/100
=> T - 293 = 0.60T
=> 0.40T = 293
=> minimum temperature,
T = 293/(0.40)
= 732.5 K
= 732.5 - 273 degrees C
= 459.5 degrees C.

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