Sonntag, Borgnakke and van Wylen
7.91 A 10-m3 tank of air at 500 kPa, 600 K acts as the high-temperature reservoir for a Carnot heat engine that rejects heat at 300 K. A temperature difference of 25°C between the air tank and the Carnot cycle high temperature is needed to transfer the heat. The heat engine runs until the air temperature has dropped to 400 K and then stops. Assume constant specific heat capacities for air and find how much work is given out by the heat engine. Solution: TH = Tair - 25°C TL = 300 K
AIR QH HE QL 300 K
W
P1V 500 × 10 mair = RT = = 29.04 kg 1 0.287 × 600 TL dW = ηdQH = 1 - T - 25 dQH air dQH = -mairdu = -mairCvdTair
TL Ta2-25 ⌠ W=⌡ ⌠dW = -mairCv1 - T -25dTa = -mairCvTa2-Ta1-TL ln T -25 a a1 ⌡ 375 = -29.04 × 0.717 × 400 - 600 - 300 ln 575 = 1494.3 kJ