TFS · Thermodynamics · Problem 30PDFSolution in PDF ↓
TFS · Thermodynamics · Problem 30
Problem & Solution
Video Synthesis
Topic: Brayton cycle (gas turbine thermodynamics) — In a Brayton cycle, 70 degree atmospheric air enters the compressor with a pressure ratio 5 to 1.
Approach: So let's start by talking about what exactly a Brayton cycle is.
Formula reference: formula a bit where we say T4 over T3 equals P4 over P3.
Key values: 530 rankin, 839.4 rankin
Reference: reference handbook
✅ Answer: B
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Student questions asked in live office hours about this problem
OH 113
Q: Why is the Brayton cycle efficiency equation different in your notes versus the reference handbook, and when should we include/exclude Q-dot terms? Also, why can we assume constant CP in the air tables when CP actually varies with temperature and pressure at each stage?
A: For the constant CP assumption: that's valid when the problem states ideal gas behavior—then you can relate enthalpy differences to temperature differences using constant specific heat (H = CP·ΔT). On the efficiency formulas: we're actually saying the same thing. The handbook writes W_net as work_12 (negative, into compressor) plus work_34 (positive, out of turbine), but I prefer working with positive numbers, so I subtract them as W_34 - W_12. The underlying physics is identical.