PHYS 201 Lecture 11: Heat Engines

Overview of Lecture 11 on Heat Engines

• Focus is on PHYS 201 General Physics 3, instructed by Prof. Matt Leifer.
• Homework 2 deadlines got extended due to ProbView issues; peer reviews are due March 13 (Thu), and corrections are due March 18 (Tue).
• Reading assignment for Thursday includes Openstax, University Physics, Chapter 14, Fluid Mechanics, Sections 14.1–14.4
• A reading quiz is due Wednesday at 12 noon.
• There is a Build-Your-Own Bennet Fidget Toy event happening Tuesday, March 18 at 7:00 PM in AF 206A with the Chapman Physics Club
• There are multiple conferences happening in the next 3 weeks
  • Q 100: Examining Quantum Foundations 100 Years On, March 12-14, Killefer Building
  • American Physical Society Global Summit, March 15-21, Anaheim Convention Center
  • Knowledge and Agency in Quantum Mechanics, March 24-25, Killefer Building
• Public Physics Events are available
  • Fernando Sols will speak on Thursday March 13 at 5:30pm in Agyros Forum 212
  • Saturday March 15, Quantum Jubilee, The Grove Anaheim

Cyclic Processes

• These processes restore the system to its initial macrostate repetitively.
• Environments are often considered heat reservoirs with constant macrostates.

Perpetual Motion Machines

• These hypothetical devices sustain motion indefinitely in a cyclic process without an external energy source.
• First Kind: Creates energy from nothing, violating energy conservation and the first law of thermodynamics
• Second Kind: Extracts energy by decreasing the entropy of an isolated system, violating the second law of thermodynamics.

Heat Engines

• Heat engines extract heat from a reservoir during a cyclic process to perform mechanical work.
• A perfect heat engine converts all extracted heat into mechanical work.
• Perfect heat engines cannot exist because they violate the 2nd Law of Thermodynamics and are akin to perpetual motion machines of the second kind.
• Key aspects include computing entropy changes in a cycle, where the engine returns to its initial macrostate, and heat extraction decreases entropy in the reservoir.
• Isolated engine-reservoir systems have implications

Real Heat Engines

• Additional processes are needed to increase environmental entropy, avoiding violations of the second law.
• A cold reservoir is added to increase its entropy by dumping heat from the engine.
• These exploit heat flow from hot to cold reservoirs, extracting some energy for work.
• Example of a Real Heat Engine:
  • Steam turbine in a power plant uses a hot reservoir (burning fuels, nuclear power) to boil water into steam
  • Steam expands against turbine blades turning a generator
  • Used steam goes to a condenser (cold reservoir) to release heat, condense back into water, and repeat the cycle

Efficiency of Heat Engines

• Efficiency is defined
• For cyclic processes, efficiency per cycle equals efficiency over multiple cycles.
• Over the cycle, Efficiency can be determined via the first law of thermodynamics

Maximal Efficiency

• Perfect engines with infinite capacity and zero waste are impossible
• Engines return to their original state after each cycle
• The hot reservoir's entropy decreases while the cold reservoir's entropy increases
• The engine + hot reservoir + cold reservoir constitutes an isolated system, governed by the second law of thermodynamics
• The derived bound applies universally to heat engines exploiting heat flow between temperatures
• Efficiency is capped by reservoir temperatures and is independent of the engine's design
• Most real heat engines are far from maximally efficient due to the tradeoff between efficiency and power

Consequences of Thermodynamics

• Any temperature difference can theoretically generate mechanical energy.
• Greater temperature differences lead to more efficient heat engines.
• Energy waste is inevitable.
• Limited by Earth's naturally occurring temperatures in practice.
• Historical power plants dumped heat into rivers, most now use cooling towers
• Cities retaining environmental heat are hotter than surroundings
• Waste heat from human activities in basins, like Los Angeles', can exceed the basin's solar energy intake
• Burning fossil fuels for energy increases temperatures with environmental consequences

Efficiency of Nuclear Power Plants

• Nuclear fission power plants are the most efficient power generators because of the amount of energy produced
• Reactor cores produce pressurized steam, but higher Temps would melt the fuel rods
• Cooling towers are required
• Real reactors get about one third efficiency
• Generating requires heat absorption and waste heat dumping
• Roughly two-thirds of fuel energy is wasted
• Waste heat disposal can warm rivers or evaporate tons of water per second in cooling towers

Natural Energy Differences

• Exploiting natural temperature differences (geothermal, solar, wind) avoids significant environmental heating
• Smaller natural temperature differences result in lower efficiencies
• Larger heat engines are needed to maintain energy production rates
• Deserts, like those in California, are often used

Refrigerators

• Refrigerators are heat engines in reverse
• The second law implies heat won't spontaneously flow from cold to hot reservoirs
• Continuous work is required to cause this reverse flow and extracting heat from the cold reservoir maintains its low temperature.

Household Refrigerator

• The cold reservoir in a household refrigerator is where the food is stored.
• An "engine" uses refrigerant flowing through tubes.
• This substance evaporates at room temp but condenses via compression

Coefficient of Performance

• Fridge quality is quantified via coefficient of performance (COP)
• Equations for best COP are available

The Carnot Cycle

• This cycle provides optimal efficiency for heat engines.
• Requires isothermal expansion, adiabatic expansion, isothermal compression & adiabatic compression
• Efficiency calculation involves heat exchanged with hot and cold reservoirs during isothermal phases.
• Isothermal expansion is Phase 1
• Isothermal compression is another key phase
• Carnot cycle phases include adiabatic processes
• Dividing equations reveals efficiency

Alternative Cycles

• Carnot cycle has maximal efficiency but low power.
• Its processes (especially isothermal) have to be close to the equilibrium, so cycles are very slow.
• The per-cycle work (area inside PV diagram) is low
• Isochoric or isobaric processes replace isotherms in practice.