A typical coal-fired power plant burns metric tons of coal every hour to generate of electricity. metric ton = . The density of coal is 1500 kg/m3 and its heat of combustion is . Assume that all heat is transferred from the fuel to the boiler and that all the work done in spinning the turbine is transformed into electric energy.
a. Suppose the coal is piled up in a room. How tall must the pile be to operate the plant for one day?
b. What is the power plant’s thermal efficiency?
(a) The plant of one day
(b) The power plant's thermal efficiency is
Let be the volume of the heaped coal. It is obvious that since the base is a square; let's call one of its sides and the height.
The rate at which the fuel must be consumed for the power plant to operate is indicated in metric tones per hour. This will be symbolized by the letter . It's obvious that if we want the power plant to run for hours, the amount of coal we'll need to burn is.
A mass of a volume of coal with density will be
Therefore, we can combine our formulas to find:
We know that the mass required for our power plant in one hour is 300 metric tones,
The efficiency is given by,
This is generated by multiplying the numerator and denominator by the time, where the output electric power is denoted by and the input heating power is denoted by . We know that when mass of a substance with specific energy is burned, heat is generated.
This means that we'll need to burn the same fuel at a rate of to acquire heating power .
A mass of metric tons is needed in one hour. That is, our efficiency will be
Using a numerical approach, we have
The coefficient of performance of a refrigerator is . The refrigerator's compressor uses of electric power and is efficient at converting electric power into work. What are (a) the rate at which heat energy is removed from inside the refrigerator and (b) the rate at which heat energy is exhausted into the room?
A car’s internal combustion engine can be modeled as a heat engine operating between a combustion temperature of 1500oC and an air temperature of 20oC with 30% of the Carnot efficiency. The heat of combustion of gasoline is 47kJ/g. What mass of gasoline is burned to accelerate a 1500kg car from rest to a speed of 30 m/s?
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