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Chapter 24: Problem 15

Calculate the efficiency of a fossil-fuel power plant that consumes 382 metric tons of coal each hour to produce useful work at the rate of \(755 \mathrm{MW}\). The heat of combustion of coal is \(28.0 \mathrm{MJ} / \mathrm{kg}\).

Short Answer

Expert verified
The efficiency of the coal-fired power plant is 25.4%.

Step by step solution

01

Calculate the Total Energy Input Per Hour

To calculate the total energy input into the power plant per hour, we need to convert the mass of consumed coal into energy. We can do this using the heat of combustion, which is the amount of energy released when a specific amount of coal is burned. Given that the heat of combustion of coal is 28.0 MJ/kg and that the plant consumes 382 metric tons of coal per hour, we calculate the total energy input per hour as follows: \(382,000\,\mathrm{kg/hour} \times 28.0\,\mathrm{MJ/kg} = 10,696,000\,\mathrm{MJ/hour}\). This is equivalent to \(10,696,000\,\mathrm{MJ/hour} \div 3600 \, \mathrm{s/hour} = 2971.11 \, \mathrm{MW}\).
02

Calculate the Efficiency of the Power Plant

Efficiency is defined as the ratio of useful work output to the total energy input. The data provided states that the useful work produced is 755 MW. Using our calculated total energy input from Step 1, we can now find the efficiency of the power plant: \( \frac{755 \, \mathrm{MW}}{2971.11 \, \mathrm{MW}} = 0.254 = 25.4%\).

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Most popular questions from this chapter

A mixture of \(1.78 \mathrm{~kg}\) of water and \(262 \mathrm{~g}\) of ice at \(0{ }^{\circ} \mathrm{C}\) is, in a reversible process, brought to a final equilibrium state where the water/ice ratio, by mass, is \(1: 1\) at \(0^{\circ} \mathrm{C} .(a)\) Calculate the entropy change of the system during this process. (b) The system is then returned to the first equilibrium state, but in an irreversible way (by using a Bunsen burner, for instance). Calculate the entropy change of the system during this process. (c) Show that your answer is consistent with the second law of thermodynamics.

A refrigerator does \(153 \mathrm{~J}\) of work to transfer \(568 \mathrm{~J}\) of heat from its cold compartment. (a) Calculate the refrigerator's coefficient of performance. ( \(b\) ) How much heat is exhausted to the kitchen?

In a refrigerator the low-temperature coils are at a temperature of \(-13^{\circ} \mathrm{C}\) and the compressed gas in the condenser has a temperature of \(25^{\circ} \mathrm{C}\). Find the coefficient of performance of a Carnot refrigerator operating between these temperatures.

How much work must be done to extract \(10.0 \mathrm{~J}\) of heat \((a)\) from a reservoir at \(7^{\circ} \mathrm{C}\) and transfer it to one at \(27^{\circ} \mathrm{C}\) by means of a refrigerator using a Carnot cycle; \((b)\) from one at \(-73^{\circ} \mathrm{C}\) to one at \(27^{\circ} \mathrm{C} ;(c)\) from one at \(-173^{\circ} \mathrm{C}\) to one at \(27^{\circ} \mathrm{C} ;\) and \((d)\) from one at \(-223^{\circ} \mathrm{C}\) to one at \(27^{\circ} \mathrm{C} ?\)

Four moles of an ideal gas are caused to expand from a volume \(V_{1}\) to a volume \(V_{2}=3.45 V_{1} .(a)\) If the expansion is isothermal at the temperature \(T=410 \mathrm{~K}\), find the work done on the expanding gas. ( \(b\) ) Find the change in entropy, if any. ( \(c\) ) If the expansion is reversibly adiabatic instead of isothermal, what is the entropy change?
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