Final question in my physics course...pls help :/ Suppose a power plant delivers

Question

Final question in my physics course...pls help :/

Suppose a power plant delivers energy at 835 MW using steam turbines. The steam goes into the turbines superheated at 566 K and deposits its unused heat in river water at 284 K. Assume that the turbine operates as an ideal Carnot engine.
a. If the river flow rate is 35.2 m3/s, calculate the average temperature increase (in Celsius) of the river water downstream from the power plant.
b. What is the entropy increase per kilogram of the downstream river water?

Explanation / Answer

PROPS GOES TO "ZANTHYMX" Treating power plant like idealCarnot Engine, its efficiency will be: {Efficiency} = e = 1 - {T2/T1} = = 1 - {(286 K)/(558 K)} = 0.487455 Item(a): Given that power plant delivers power {P = 951 MW= 951.0e+6W}, and that efficiency is{e =0.487455}, total heat power discardedinto river is given by: {Heat Power Discarded} = PQ = {P/e}- P = = {(951.0e+6)/(0.487455)}- (951.0e+6) = 10.0e+8 W Since river water has specific heat {C = 4184Joules/kg/degK}, and given that river mass flow rate {MFR = ?*VFR = (1000 kg/m^3)*(36.3 m3/s} = (36.3e+3 kg/s)}, we obtain: ?T = {PQ}/{C*MFR} = = {10.0e+8}/{(4184)*(36.3e+3)} = 6.584 degC Item(b): River water gains heat power {PQ =10.0e+8 W} while increasing its temp by {?T = 6.584 degK}. From definition of entropy"S" for river mass "M" of water: ?S/M = (1/M)? dQ/T = = (1/M) ?T1T2 {M*C*dT}/T = (C)*Loge{T2/T1} = (4184)*Loge{(286 + 6.584)/(286)} = 95.23 Joules/kg/degK

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