HVAC · Thermodynamics · Problem 15PDFSolution in PDF ↓
HVAC · Thermodynamics · Problem 15
Problem & Solution
Video Synthesis
Problem: in a Carnot heat pump are 22 evaporates at 31 psi A and condenses at 211 psi A.
Given: 15 in a Carnot heat pump are 22 evaporates at 31 psi A and condenses at 211 psi A; 31 PSI is about halfway between 20...
Approach: Since the Carnot heat pump we want to use the temperatures to find the COP, but we only know the pressure.
Key formula: formula for a Carnot heat pump, which is TH over TH minus TL
Calc: And we know that it's using R22.
Calc: So let's look up R22 and see if we can find the high and low temperature that correspond to these high and low pressures.
Result: And that works out to 5.1 which is answer choice C.
Office Hours
2
Student questions asked in live office hours about this problem
OH 88: HVAC: Thermo Module #15
Q: Does a problem have to explicitly state it's a Carnot cycle in order to use the Carnot COP equations for heat pumps and refrigerators?
A: The problem doesn't have to say 'Carnot' but it must indicate maximum theoretical efficiency or use similar keywords—you can't just use these equations for any heat pump or refrigerator just because temperatures are given. For regular cycles, you need actual values like QH, QL, or compressor work instead.
OH 106: HVAC: Thermo Module #15
Q: How can we use the pH diagram and enthalpy to solve for COP in a heat pump cycle, especially when the cycle differs from a Carnot cycle?
A: For Carnot COP, you only need temperatures—use the pH diagram to identify T_LO (constant temperature in the evaporator, states 1-4) and T_HI (constant temperature inside the vapor dome at state 3, where the phase change and significant heat transfer occur). The sensible heat transfer in the superheated region is negligible, so the magic happens in the two-phase region where you should read your temperatures from.