A typical coal-fired power plant generates 1000 MW of usable power at an overall thermal efficie

step 1 So for this problem, starting off with part A, we have QH is equal to W over E. And so pH is equ

A typical coal-fired power plant generates 1000 MW of usable...

A typical coal-fired power plant generates $1000 \mathrm{MW}$ of usable power at an overall thermal efficiency of $37 \%$. (a) What is the rate of heat input to the plant? (b) The plant burns anthracite coal, which has a heat of combustion of $2.65 \times 10^{7} \mathrm{~J} / \mathrm{kg} .$ How much coal does the plant use per day, if it operates continuously? (c) At what rate is heat ejected into the cool reservoir, which is the nearby river? (d) The river is at $18.0^{\circ} \mathrm{C}$ before it reaches the power plant and $18.4^{\circ} \mathrm{C}$ after it has received the plant's waste heat. Calculate the river's flow rate, in cubic meters per second. (e) By how much does the river's entropy increase each second?

Key Concepts

Thermal Efficiency

Thermal efficiency is the ratio of usable output energy to total input heat energy in a power plant. It reflects the effectiveness of converting the energy stored in a fuel into electrical energy and is a fundamental parameter in assessing the performance of energy conversion systems.

Heat Input Calculation

Calculating the rate of heat input involves determining the total energy supplied to the power plant based on its thermal efficiency and the electrical power output. This concept connects the energy input needed from fuel combustion to achieve the specified output, taking losses into account.

Combustion Energy and Fuel Consumption

The combustion energy concept pertains to the energy released per unit mass of fuel burned, which is essential for calculating how much fuel is needed for a given energy output. It bridges thermodynamic energy calculations with practical operational aspects such as daily fuel consumption rates.

Waste Heat Rejection and Conservation of Energy

The principle of waste heat rejection arises from the conservation of energy, where not all the input heat is converted into useful work. The rejected heat, typically dumped into a reservoir or environment, is a critical part of the energy balance in a thermal system and must be managed for both efficiency and environmental impact.

Energy Balance in Heat Exchangers and Flow Rate Calculations

Determining the flow rate of a cooling medium, such as river water, requires applying the energy balance equation. This involves equating the waste heat energy to the product of the mass flow rate, specific heat capacity, and temperature increase of the cooling water, which is a key concept in heat transfer and thermal system design.

Entropy Increase in Thermal Systems

The increase in entropy in a thermal system, especially in waste heat disposal processes, is an important concept in the second law of thermodynamics. It quantifies the degree of irreversibility associated with the energy conversion process and environmental heat discharge, highlighting the natural tendency towards increased disorder.

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