TFS · Thermodynamics · Problem 10PDFSolution in PDF ↓
TFS · Thermodynamics · Problem 10
Problem & Solution
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- Problem: 50 pounds per second of 60 degree ideal air with constant specific heats is compressed with a 70% efficient compressor.
- Approach: In order to find the power we would normally do an m dot delta h.
- Key step: 50 pounds per second of 60 degree ideal air with constant specific heats is compressed with a 70% efficient compressor.
- Watch out: We need to know the temperature of the leaving air and it's not 100% efficient so we cannot assume an isentropic process.
- Result: And it's closest to answer choice C.
- ✅ Answer: C
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Student questions asked in live office hours about this problem
OH 90
Q: When should we look for Cp at the actual temperature versus using the room-temperature value of 0.24 BTU/(lbm·°R)? With a 500°F temperature rise, I'd be hesitant to assume the room-temp value applies.
A: Your instinct is good, but on the PE exam the answer choices are usually spaced far enough apart that even a 10% variation in Cp won't change which answer you pick. For air in the range of typical PE problems, Cp = 0.24 is a reliable constant unless the problem specifically provides a different value or table to use. If you're ever uncertain, scan the problem for whether Cp data is given — if it is, use it; if it isn't, 0.24 is the expected assumption.
OH 112
Q: I found the right formulas but don't understand the compression ratio — the handbook defines it only in terms of volume, but in the solution you use P1/P2 as the compression ratio from an isentropic constant-entropy process equation. Why can we assume that?
A: Compression ratio is typically defined as V1/V2 (inlet volume over outlet volume), but for an isentropic process with an ideal gas, pressure and volume are related by PVᵞ = constant — so P1/P2 = (V2/V1)ᵞ, which means the pressure ratio and volume ratio are not independent. When we say 'compression ratio' in the context of an isentropic process equation, we're using the isentropic relationship to convert between pressure ratio and volume ratio as needed. The two are interchangeable once you know the isentropic exponent.