A power plant, having a Carnot efficiency, produces 1.00 GW of electrical power from turbines th

step 1 Here, tc is equal to 1 minus tc y tch. That is equal to work done of engine divided by the modul

A power plant, having a Carnot efficiency, produces 1.00 GW...

A power plant, having a Carnot efficiency, produces $1.00 \mathrm{GW}$ of electrical power from turbines that take in steam at $500 \mathrm{K}$ and reject water at $300 \mathrm{K}$ into a flowing river. The water downstream is $6.00 \mathrm{K}$ warmer due to the output of the power plant. Determine the flow rate of the river.

Key Concepts

Heat Transfer and Specific Heat Capacity

Heat transfer involves the movement of thermal energy from one body or substance to another due to a temperature difference. Specific heat capacity is a material property that indicates the amount of heat required to change the temperature of a unit mass of a substance by one degree. These principles are used to determine how much heat energy is needed to raise the temperature of the river water by a specified amount, linking the waste heat output of the power plant to the resulting temperature increase in the environment.

Mass Flow Rate Calculation

Mass flow rate calculation connects the energy transferred to an amount of substance that undergoes a temperature change. By applying the relation Q = m*c*?T, where Q is the heat energy, m is the mass, c is the specific heat capacity, and ?T is the temperature change, one can determine the required flow rate (mass per unit time) of the river water that absorbs the waste heat. This concept ties together the energy concerns of the power plant’s operation with environmental impact assessments.

Heat Engine Energy Conversion

Heat engine energy conversion refers to the process through which thermal energy is transformed into mechanical work. The efficiency of this conversion is determined by the fraction of input heat energy that is converted into useful work, with the remainder typically being expelled as waste heat. In the context of a power plant, this concept is crucial for evaluating how much heat must be input to generate a given amount of electrical power.

Carnot Efficiency

Carnot efficiency represents the maximum theoretical efficiency possible for a heat engine operating between two thermal reservoirs. It is defined by the temperatures of the hot and cold reservoirs (in absolute units) and establishes an ideal limit: no real engine can be more efficient. This concept is central in understanding the energy conversion limits in power plants and the unavoidable waste of heat energy due to the temperature difference between the high-temperature source and the low-temperature sink.

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