A 32% efficient electric power plant produces 900 MJ of electric energy per seco

Question

A 32% efficient electric power plant produces 900 MJ of electric energy per second and discharges waste heat into 200C ocean water. Suppose the waste heat could be used to heat homes during the winter instead of being dischargesd into the ocean. A typical American house requires an average of 20 kW for heating. How many homes could be heated with the waste heat of this one power plant?

***The answer is supposed to be 30,000 homes but I am not sure how to get there. The plant produces 900 MJ not 900MW like the other question that is very similar to this question already posted on this site.

Explanation / Answer

Given,

Power produced by power plant @32% efficiency = 900 MW

(Since, plant producing 900 MJ/s and J/s is power, so in this case, 900 MJ/s = 900 MW)

you are considering total power generated by plant is 900 MJ/s and you are then calculating useful power output by multiplying it by 32% efficiency, while, in given case, 900 MJ/s is the useful output, so total plant output has to be calculated by dividing it by 0.32

Total Plant output = 900/0.32 = 2812.5 MW

Waste heat = 2812.5 - 900 = 1912.5 MW

So, the number of homes = 1912.5 MW/ 20 = 95625 homes

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