HVAC · Thermodynamics · Problem 23PDFSolution in PDF ↓
HVAC · Thermodynamics · Problem 23
Problem & Solution
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Problem: Thermal 23, 500 pounds per hour of superheated steam at 900 degrees and 500 psi a enters a turbine and expands to atmospheric pressure.
Given: 500 pounds per hour of superheated steam at 900 degrees and 500 psi a enters a turbine and expands to atmospheric pre...
Approach: The turbine is 70% efficient and powers a 90% efficient generator was the output power.
Calc: So you have this steam entering at 900 degrees Fahrenheit and 500 psi.
Calc: So the way to analyze a turbine is to say q dot equals m dot delta h delta h being h1 minus h2.
Result: So B2's per hour will cancel and we will end up with units of KW and the magnitude works out to 32.8 KW which is closest to answer choice B.
Office Hours
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Student questions asked in live office hours about this problem
OH 15: Thermo 23
Q: Why do we multiply the turbine work by the 90% generator efficiency instead of dividing by it? Shouldn't a 90% efficient generator require more input power to produce the same output?
A: You multiply because you're tracking energy losses sequentially: the turbine produces 70% of its ideal work as shaft work, and then the generator converts 90% of that shaft work into electrical power. We're not working backwards from a power requirement—we're calculating forward from the turbine output to the final electrical power, so each efficiency step is a multiplication.
OH 56: HVAC: Thermo #23
Q: If the entropy value falls outside the superheated tables at 14.7 PSIA, is that sufficient to assume a saturated mixture, or are there other considerations for when to use saturated mixture tables?
A: Yes, if the entropy doesn't meet the superheated region threshold, it's safely a saturated mixture (unlikely to be subcooled in turbine applications). Once you confirm it's saturated, use the entropy boundaries (SF and SG) to calculate quality: Q = (S2 - SF) / SFG, then determine other properties from that quality value.
OH 63: HVAC: Thermo #23
Q: Are the isentropic efficiency formulas for compressors and turbines using enthalpy available in the Reference Handbook, or does it only show temperature-based versions?
A: The Handbook doesn't include the enthalpy version, but you should know it anyway—it's actually more fundamentally correct than the temperature version. For an ideal gas with constant specific heats, you can convert between enthalpy and temperature formulations since ΔH = CP·ΔT, so efficiency can be expressed as the ratio of actual enthalpy change to isentropic enthalpy change.
OH 95: HVAC: Thermo Module #23
Q: Why did you calculate H2 prime (actual leaving enthalpy) using the isentropic assumption instead of just finding ideal enthalpies and applying the 0.7 turbine efficiency and 0.9 generator efficiency as multipliers?
A: You have to use the isentropic assumption to find H2 ideal from the steam tables first—that's a required step. Once you know H1, H2 ideal, and the turbine efficiency, you can then solve for H2 prime (actual). This is the only rigorous way to handle turbine problems; if you're already comfortable with the method, you can combine steps to move faster, but the underlying approach is necessary.