What is the rate of heat input to the plant? The plant burns anthracite coal, wh

Question

What is the rate of heat input to the plant? The plant burns anthracite coal, which has a heat of combustion of 2.65 x 10^7 J/kg. How much coal does the plant use per day? At what rate is heat ejected into the cool reservoir, which is the nearby river? The river's temperature is 18.0 degrees celsius before it reaches the power plant and 18.5 degrees celsius after it has received the plant's waste heat. Calculate the river's flow rate, in m^3 per second. What is the change in the entropy of the river?

Explanation / Answer

Heat energy supplied = 1000*106/0.4 = 2500*106 W

Coal consumption = 2500*106/2.65*107 = 94.34 kg/s

Daily coal consumption = 94.34*(60*60*24) = 8150943 kg

Rate of heat rejection = 2500 - 1000 = 1500 MW

Specific heat of water Cp = 4180 J/kg-K

Heat supplied to river = mCp(T2-T1)

So, 1500*106 = m*4180*(18.5-18)

m = 717703 kg/s

Density of water = 1000 kg/m3

So Flow rate = 717703/1000 = 717.7 m3/s

Change in entropy = Q/T = 1500*106/(273+18.5) = 5.146 MJ/K-s

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