Ina fossil fuel power plant 1.0 t of coal is combusted per hour(combustion value
ID: 1815628 • Letter: I
Question
Ina fossil fuel power plant 1.0 t of coal is combusted per hour(combustion value 32.8 MJ kg-1). The steam temperature is400°C. The waste heat is transferred to a river with a watertemperature of 15°C. (a) What would the thermal efficiency ofthe power plant be if it worked as efficiently as a Carnot cycle?Would the efficiency be significantly affected by a 5 K temperaturechange of the water temperature in the river? (b) What is the powerobtained from the heat of combustion assuming that the actualefficiency is 70% of the Carnot efficiency? (c) How much heat istransferred into the river (per hour)?
Explanation / Answer
a) carnot efficiency = 1 - TC/TH = 1 - (15 + 273) K/ (400 + 273) K =0.572065379 => 57.2 % if 5K change in water temperature, efficiency barely changes if Twater = 10 C eff = 1 - (10 + 273) / ( 400 + 273) = 0.579494799 => 57.9 % if T water = 20 C eff = 1 - (20 + 273) / (400 + 273)= 0.564635958 => 56.5 % b) QH = 1 metric ton * ( 1000 kg /1 metric ton) * (32.8 MJ/kg) = 32800MJ (per hour) Power obtained = Carnot efficient* 70% efficiency * QH power obtained = 0.572 * 0.70 * (32800 MJ/hr) = 13133.12MJ/hr = 1.31 x 104 MJ/hr c) QC = QH - W = 32800 - 13133.12 = 19666.88 = 1.97 x104 MJ/hr