An electrical power plant has an overall efficiency of 15 %....

An electrical power plant has an overall efficiency of $15 \%$. The plant is to deliver $150 \mathrm{MW}$ of electrical power to a city, and its turbines use coal as fuel. The burning coal produces steam at $190^{\circ} \mathrm{C}$, which drives the turbines. The steam is condensed into water at $25^{\circ} \mathrm{C}$ by passing through coils that are in contact with river water. (a) How many metric tons of coal does the plant consume each day $\left(1\right.$ metric ton $\left.=1 \times 10^{\circ} \mathrm{kg}\right) ?$ (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 $20^{\circ} \mathrm{C}$, at what minimum rate must it flow over the cooling coils so that its temperature doesn't exceed $25^{\circ} \mathrm{C}_{?}^{\circ}$ (Note: The heat of combustion of coal is $7.8 \times 10^{3} \mathrm{cal} / \mathrm{g}$.)

An electrical power plant has an overall efficiency of $15 \%$. The plant is to deliver $150 \mathrm{MW}$ of electrical power to a city, and its turbines use coal as fuel. The burning coal produces steam at $190^{\circ} \mathrm{C}$, which drives the turbines. The steam is condensed into water at $25^{\circ} \mathrm{C}$ by passing through coils that are in contact with river water. (a) How many metric tons of coal does the plant consume each day $\left(1\right.$ metric ton $\left.=1 \times 10^{\circ} \mathrm{kg}\right) ?$ (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 $20^{\circ} \mathrm{C}$, at what minimum rate must it flow over the cooling coils so that its temperature doesn't exceed $25^{\circ} \mathrm{C}_{?}^{\circ}$ (Note: The heat of combustion of coal is $7.8 \times 10^{3} \mathrm{cal} / \mathrm{g}$.)

Key Concepts

Efficiency in Power Generation

This concept refers to the ratio of useful energy output to the total energy input of a system. In power plants, efficiency determines how much fuel is needed to produce a given amount of electrical power, making it essential for both performance evaluation and fuel consumption analysis.

Energy and Power Calculations

Understanding the relationship between power (the rate of energy transfer) and total energy over time is crucial. This involves converting power ratings into energy quantities by considering the time of operation, which is necessary for determining fuel requirements and system performance over extended periods.

Fuel Calorific Value and Consumption

Fuel calorific value is a measure of the energy released per unit mass of fuel when it is combusted. This concept is key to calculating the total mass of fuel required to deliver a specified energy output, linking the quality of the fuel to the overall efficiency of the power plant.

Heat Transfer and Cooling Requirements

Heat transfer principles, including the concept of specific heat capacity and energy balance, are used to determine the necessary rate of cooling in systems that must dissipate excess thermal energy. This ensures that the cooling medium does not exceed temperature limits while absorbing the residual heat from the power generation process.

Economic Analysis of Fuel Use

Economic analysis in energy systems involves calculating the cost of fuel consumption based on the quantity of fuel required and the unit price of the fuel. This financial assessment helps in understanding the operational costs and economic feasibility of power generation methods.

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