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Suppose a power plant delivers energy at 951 MW using steamturbines. The steam goes into the turbines superheated at 558 K anddeposits its unused heat in river water at 286 K. Assume that theturbine operates as an ideal Carnot engine. a) If the river flow rate is 36.3 m³/s, calculatethe average temperature increase (in Celsius) of the river waterimmediately downstream from the power plant.

Answer :

Final answer:

The average temperature increase of the river water downstream from the power plant is 131.85 K.

Explanation:

To calculate the average temperature increase of the river water downstream from the power plant, we can use the Carnot efficiency formula. The efficiency of a Carnot engine is given by the equation: efficiency = 1 - (Tc/Th), where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir. In this case, the temperature of the river water is the temperature of the cold reservoir, which is 286 K, and the temperature of the steam entering the turbines is the temperature of the hot reservoir, which is 558 K.

The temperature increase of the river water can be calculated by multiplying the temperature difference between the hot and cold reservoirs by the efficiency of the Carnot engine. The temperature difference is

Th - Tc = 558 K - 286 K

= 272 K.

The efficiency of the Carnot engine can be calculated as

1 - (Tc/Th) = 1 - (286/558)

= 0.4844.

Therefore, the average temperature increase of the river water immediately downstream from the power plant is

272 K * 0.4844 = 131.85 K.

Learn more about Carnot efficiency here:

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