Thermodynamic Cycles

In one line: A heat pump or refrigerator uses work to move heat from cold to hot. Thermodynamics says how much heat a unit of work can move at best, and every real machine falls short of that limit.

Core idea

Power plants, engines, refrigerators and heat pumps all run on cycles: a working fluid passes through a series of processes and returns to its starting state. Two laws govern every one of them [1]:

• The first law: energy is conserved, so the heat in, the heat out and the work balance.
• The second law: heat flows naturally only from hot to cold, and every real process generates entropy. So there is a hard ceiling, the Carnot limit, on performance.

How it works

The vapor-compression cycle, used in refrigerators, air conditioners and heat pumps, has four steps:

1. Evaporator: the cold, low-pressure refrigerant boils, absorbing heat from the space being cooled.
2. Compressor: work raises the vapor’s pressure and temperature.
3. Condenser: the hot vapor condenses, rejecting heat to the warm side.
4. Expansion valve: the liquid is throttled back to low pressure and temperature.

Measuring performance. The coefficient of performance (COP) compares the useful heat with the work put in. For a heat pump:

$CO{P}_{HP}=\frac{Q_H}{W}CO{P}_{HP,Carnot}=\frac{T_H}{T_H-T_C}$

Temperatures are absolute, in kelvin. Example: heating a house to 20 °C (293 K) from 0 °C (273 K) outdoors gives a Carnot COP of about 15. Real heat pumps achieve 2 to 4, because of compressor losses, the temperature differences needed to push heat through the heat exchangers, and throttling. Performance also falls as the temperature lift grows.

Cooling capacity is often quoted in tons of refrigeration: one ton is 12,000 Btu/h, about 3.5 kW.

In practice

The course project uses a spacecraft heat pump study [2]. Satellites normally reject waste heat by radiating it from a panel colder than the equipment. A heat pump lifts the heat to a higher temperature, so a smaller radiator can reject it. The test unit beat its COP requirement (2.6 against 2). But the test program was cut short when particles from a compressor seal lodged in its diffuser. It is a reminder that a thermodynamic success can still fail on Reliability.

The project asks teams to redesign the cycle for higher efficiency and lower entropy generation, an open problem with no single answer.

For a leader, the main lesson is skepticism about efficiency claims. Any claim should be checked against the Carnot limit for the same temperatures, and should state where the losses are.

Questions to ask the experts

• What are the hot and cold temperatures, and what is the theoretical limit at those temperatures?
• Where are the biggest losses, in the compressor, the heat exchangers or the throttling?
• How does performance change across the operating range, not just at the design point?

Connections

• The discipline: Mechanical and Aerospace Engineering. The same bookkeeping in chemical plants: Mass and Energy Balances.
• Design choices: Trade-off Analysis. When the hardware fails: Reliability.
• Capabilities exercised: Inquiry, Connecting Across Disciplines, Ethical Actions and Integrity.

Sources

• Moran et al. (2018) Fundamentals of Engineering Thermodynamics [1]
• van Gerner, NLR heat pump study [2]

[1]

M. J. Moran, H. N. Shapiro, D. D. Boettner, and M. B. Bailey, Fundamentals of Engineering Thermodynamics, 9th ed. Hoboken, NJ, USA: Wiley, 2018.

[2]

H. J. van Gerner, “Heat Pump Conceptual Study and Design: Overall Assessment and Further Work,” National Aerospace Laboratory NLR, Rep. NLR-CR-2014-009, 2014.