A 600-MW steam power plant, which is cooled by a nearby river, has a thermal efficiency of 54 percent. Determine the rate of heat transfer to the river water. Will the actual heat transfer rate be higher or lower than this value?

Respuesta :

Answer:

[tex]\dot Q _{L} = 511.111 MW[/tex]. Heat transfer can be higher if themal efficiency is lower.

Explanation:

The heat transfer rate to the river water is calculated by this expression:

[tex]\dot Q_{L} = \dot Q_{H} - \dot W[/tex]

[tex]\dot Q_{L} = (\frac{1}{\eta_{th}}-1 )\cdot \dot W\\\dot Q_{L} = (\frac{1}{0.54}-1)\cdot (600 MW)\\\dot Q _{L} = 511.111 MW[/tex]

The actual heat transfer can be higher if the steam power plant reports an thermal efficiency lower than expected.

Following are the solution to heat transfer rate:

Work output,[tex]W = 600 \ MW[/tex]

Thermal efficiency, [tex]\eta_{th} , = 54\% = 0.54[/tex]

Using the following equation, control the rate of heat supplied to the power plant:

[tex]\eta =\frac{W}{Q_{H}} \\\\0.54=\frac{600}{Q_H}\\\\Q_H =1,111.11\ MW[/tex]

Using the following equation, calculate the rate of heat transfer to river water:

[tex]W=Q_H-Q_L\\\\600 =1,111.11-Q_L\\\\Q_L=511.11\ MW[/tex]

In actuality, the rate of heat transfer to river water will be smaller than the calculated number because some heat would be lost to the surrounding.

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