Q. 51

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### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# 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

See the step by step solution

## Step1: Find Height (part a)

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

## Step2: Find height (part b)

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,

## Step3: Find Efficiency

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