The largest topic on the exam. Properties, the first law, cycles, entropy and moist air.
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For gases far from condensing, the ideal gas law pV = mRT works; for air, R = 0.287 kJ/kg·K.
At a certain pressure, vf = 0.001 m3/kg and vg = 0.500 m3/kg. A mixture has v = 0.200 m3/kg. What is its quality?
x = (v − vf)/(vg − vf) = 0.199/0.499 = 0.40.
ThermodynamicsIdeal Gasqualitysteam tablesThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
Energy is conserved.
A compressor takes 0.5 kg/s of air from 300 K to 450 K (cp = 1.005 kJ/kg·K), with no heat loss. What power does it need?
Ẇ = ṁcpΔT = 0.5(1.005)(150) = 75.4 kW.
Common trap: (C) uses cv; steady-flow devices use enthalpy, so cp.
First Lawclosed systemsteady flowboundary workThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
A cycle’s thermal efficiency is net work over heat in.
What is the ideal Otto efficiency for a compression ratio of 9 (k = 1.4)?
η = 1 − 9−0.4 = 1 − 0.415 = 58.5%.
RankineOttoRefrigerationCoefficient of PerformanceThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
Entropy tracks irreversibility.
1 kg of water (c = 4.18 kJ/kg·K) is heated from 20 °C to 80 °C. What is its entropy change?
Δs = 4.18 ln(353.15/293.15) = 0.778 kJ/K.
Common trap: (B) uses °C in the log.
Entropyisentropicisentropic efficiencyThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
Moist air is a mix of dry air and water vapor.
Vapor pressure is 1.5 kPa and the saturation pressure at that temperature is 3.17 kPa. What is the relative humidity?
φ = 1.5/3.17 = 47%.
Psychrometrichumidity ratiorelative humidityCombustionThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
In an ideal-gas mixture each gas acts as if it filled the volume alone, so its partial pressure is pi = xip, where xi = Ni/N is the mole fraction (Dalton’s law).
A tank holds 2 kg of N2 (M = 28) and 1 kg of CO2 (M = 44) at a total pressure of 200 kPa. What is the partial pressure of the CO2?
N2: 2/28 = 0.0714 kmol; CO2: 1/44 = 0.0227 kmol. xCO2 = 0.0227/0.0942 = 0.2414, so pCO2 = 0.2414(200) = 48.3 kPa.
Common trap: (B) uses the mass fraction, 1/3; partial pressure follows the mole fraction.
Ideal Gas MixturesPsychrometricsPsychrometric ChartThat was 1 of 4 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
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