An electric power plant has an overall efficiency of 15.0%....

An electric power plant has an overall efficiency of 15.0%. The plant is to deliver 150 MW of power to a city, and its turbines use coal as the fuel. The burning coal produces steam that drives the turbines. This steam is then condensed to water at $25.0^{\circ} \mathrm{C}$ by passing it through cooling coils in contact with river water. (a) How many metric tons of coal does the plant consume each day (1 metric ton $=10^{3} \mathrm{kg} )$ ? (b) What is the total cost of the fuel per year if the delivered price is $\$ 8.00 /$ metric ton? (c) If the river water is delivered at $20.0^{\circ} \mathrm{C}$ , at what minimum rate must it flow over the cooling coils in order that its temperature not exceed $25.0^{\circ} \mathrm{C}$ ? (Note: The heat of combustion of coal is $33.0 \mathrm{kJ} / \mathrm{g} . )$

Key Concepts

Heat Transfer and Cooling Water Flow Rate

The process of condensing steam using cooling water involves transferring excess thermal energy from the steam to the water. Calculating the required flow rate of the cooling water involves using principles of heat transfer and the specific heat capacity of water, ensuring the water does not exceed its maximum allowable temperature rise.

Cost Analysis in Energy Systems

Cost analysis involves calculating the expense associated with fuel consumption based on the amount of fuel used and its unit price. This analysis is significant for economic assessments and operational planning in energy production, helping to manage the ongoing operational costs.

Heat of Combustion

The heat of combustion quantifies the amount of energy released by burning a given mass of fuel. This value is essential in converting between fuel mass and the energy produced, and it provides a basis for calculating fuel consumption in energy generation systems.

Energy Balance and Conversion

Energy balance in a power plant involves accounting for all energy inputs, outputs, and losses. By knowing the fuel's energy content and the overall efficiency, one can determine the total mass of fuel required to produce a specified amount of useful power, thereby linking fuel consumption to power output.

Overall Efficiency

Overall efficiency describes the ratio of useful output energy (or power) to the total input energy supplied from fuel. It is a key performance metric in power plants, helping to determine how effectively fuel energy is converted into electricity, and is crucial for calculating the amount of fuel required for a given power output.

Transcript

00:01 This question is about electric power plants which has an overall efficiency of 15%.

00:06 It's a coal power plant.

00:09 So it's using it's burning coal to generate electricity.

00:13 Okay, so in part a we need to find out how much coal is used every day.

00:19 So the power delivered every day.

00:25 Power delivered is 150 megawatts.

00:30 So the energy delivered per day.

00:32 K is equal to p times delta t so 150 times 10 to the 6 times 24 hours times 36 hundred seconds in each hour and you calculate this to be 1 .296 times 10 to the 13 jew so this is our w okay so qh equals to w over e so this gives 1 .296 times 10 to the 13 divide by 0 .15 and we get 8 .64 times 10 to the 13 juice.

01:23 Okay, so yeah, so we assume that the energy output by coal is all being used is qh.

01:32 So then we can calculate the mass of coal consume every day.

01:39 Okay so this is equal to qh divided by the heat of combustion of coal okay so so you just substitute substitute the numbers so qh is 8 .64 times 10 to the 13 the heat of combustion of coal is given to be 33 kilo juice per gram then you convert to kg you multiply by another thousand, okay, so such so that per kg you'll be another thousand then a factor of thousand.

02:37 So you calculate this to be 2 .62 times 10 to the 6 kg and so you have 2 .62 times 10 to the 6 kg and so you have 2 .62 times 10 to the tree are metric tons, okay, per day.

02:56 So in part a, the answer is 2 .62 times 10 to the 3 tons per day.

03:06 Then in part b, we need to calculate the cost of the fuel per year.

03:14 The cost of fuel per year.

03:22 So you are given that you are consuming each tonne 2 .62 times 10 to the tree...

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