A power plant produces electrical energy at the rate of 1300...

A power plant produces electrical energy at the rate of 1300 MW with an efficiency of 0.31 . The excess heat is dumped into a river that carries $1500 \mathrm{~m}^{3} / \mathrm{s}$ of water. How much does the river's temperature increase?

Key Concepts

Power Plant Efficiency

Power plant efficiency is the measure of how effectively a power plant converts the energy stored in fuel into useful electrical energy. It is defined as the ratio of electrical energy output to the thermal energy input, playing a critical role in determining how much excess or waste heat is generated during the process.

Energy Conservation

The principle of energy conservation states that energy cannot be created or destroyed, only transformed from one form to another. In power generation, this principle underpins calculations that equate the total input energy to the sum of the useful work done (electrical energy produced) and the waste heat released, which in turn allows for the analysis of environmental impacts such as temperature changes in nearby water bodies.

Specific Heat Capacity

Specific heat capacity is a property of a substance indicating the amount of energy required to raise the temperature of a unit mass of the substance by one degree Celsius. This concept is crucial when assessing how the dumped waste heat will affect the temperature of the river water, as it establishes the relationship between the energy absorbed by the water and its resultant temperature increase.

Mass Flow Rate

Mass flow rate is the measure of the mass of a fluid passing through a cross-section per unit time. This measurement is essential in determining how a continuous stream of water will distribute the waste heat, and thus, it is a key factor in calculating the extent to which the river's temperature will rise due to the additional thermal energy.

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