HW6b_09 solution

HW6b_09 solution - ME 18b, HW 6 Due Thursday May 21, 2009...

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1 ME 18b, HW 6 Due Thursday May 21, 2009 (accepted until 4 pm) Note: This homework is due on a Thursday not a Tuesday TAs for HW #6: Xiaobai and Julianne Number of classes attended: ______ Hours spent on homework: _______ 1. Ideal Gas Mixtures A mixture of 60% nitrogen and 40% oxygen on a molar basis is contained in a frictionless piston-cylinder assembly at 200 kPa and 175°C. The cylinder has an initial volume of 0.8 m 3 . The mixture is compressed adiabatically until the pressure reaches 450 kPa. Determine the final temperature of the mixture and the work for this process. Compare these values to air using either the cold air standard assumptions or variable specific heat method for the process. Solution: Energy Eqn. for adiabatic compression process: Q 12 – W 12 = m(u 2 – u 1 ) Since Q 12 = 0, then W 12 = mCv(T 2 – T 1 ) and T 2 = T 1 (P 2 /P 1 ) (k-1)/k where values for m, k, and Cv are based on mixture composition. working on a mass basis: c N2 = y N2 M N2 /( y N2 M N2 + y O2 M O2 ) = 0.6(28)/(0.6(28) + 0.4(32)) then c N2 = 0.57 and c N2 = 0.43 k mix = Cp mix /(Cp mix – R mix ) Cp mix = c N2 Cp N2 + c O2 Cp O2 = 0.57(1.042 kJ/kgK) + 0.43(0.922 kJ/kgK) = 0.990 kJ/kgK R mix = c N2 (R/M N2 ) + c O2 (R/M O2 ) = 0.57(8.314/28) + 0.43(8.314/32) = 0.281 kJ/kgK Cv mix = Cp mix - R mix = (0.990 – 0.281) = 0.709 kJ/kgK k mix = 0.990/0.709 = 1.396 T 2 = 448K(450/200) 0.396/1.396 T 2 = 564 K or 291°C m = PV/RT = (200 kPa·0.8 m 3 )/(0.281 kPa m 3 /kgK·448K) = 1.27 kg W 12 = (1.27 kg)(0.709 kJ/kgK)(564 – 448)K; W 12 = 104 kJ
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2 Isentropic compression process, cold-air std assumption: T 2 = T 1 (P 2 /P 1 ) (k-1)/k T 2 = 448K(450/200) (0.4/1.4) = 565 K or 292°C W 12 = m(u 2 – u 1 ) = m·Cv(T 2 – T 1 ) m = PV/RT = (200 kPa·0.8 m 3 )/(0.287kPa m 3 /kgK·448K) = 1.24 kg W 12 = (1.24 kg)·(0.713 kJ/kgK)·(565 – 448)K; W 12 = 104 kJ Isentropic compression process, variable specific heat analysis:
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HW6b_09 solution - ME 18b, HW 6 Due Thursday May 21, 2009...

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