   Chapter 12, Problem 75AP

Chapter
Section
Textbook Problem

An electrical power plant has an overall efficiency of 15%. The plant is to deliver 150 MW of electrical power to a city, and its turbines use coal as fuel. The burning coal produces steam at 190°C, which drives the turbines. The steam is condensed into water at 25°C by passing through coils that are in contact with river water. (a) How many metric tons of coal does the plant consume each day (1 metric ton = 1 × 103 kg)? (b) What is the total cost of the fuel per year if the delivery price is \$8 per metric ton? (c) If the river water is delivered at 20°C, at what minimum rate must it flow over the cooling coils so that its temperature doesn’t exceed 25°C? Note: The heat of combustion of coal is 7.8× 103 cal/g.

(a)

To determine
The consumption of coal by the plant in metric ton every day.

Explanation

Given Info:

The efficiency of the plant is 15% .

Output of the plant is 150MW .

Temperature of the steam is 190°C

The heat of combustion of coil is 7.8×103cal/g

Formula to calculate the consumption of coil in each day is,

ΔmΔt=PinHc (I)

• Pin is the power given to the plant by burning the coal
• Hc is the heat of combustion

Since the power input to the plant is,

Pin=Poute

• Pout is the power output from the plant

Thus, equation (I) is given by

ΔmΔt=Pout/eHc

Substitute 150MW for Pout , 15% for e and 7

(b)

To determine
The total cost of the fuel per year.

(c)

To determine
The minimum rate of flow over the cooling coils.

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