ENGG 116: Thermodynamics Lecture #10 - Machines & Efficiency

Concepts of Thermodynamics

  • Focuses on machines and efficiency related to thermodynamics, specifically discussing various cycles.

Zeroth Law of Thermodynamics

  • If system A is in thermal equilibrium with system B, and B with C, then A is in thermal equilibrium with C.

Laws of Thermodynamics

  1. First Law: Energy cannot be created or destroyed, only transformed.
  2. Second Law: The entropy of the universe always increases during a spontaneous process.

Energy Balance Equation

  • The equation for energy balance in a system:
    [(Q{in} - Q{out}) + (W{in} - W{out}) + (E{mass,in} - E{mass,out}) = \Delta U + \Delta KE + \Delta PE]

Heat Transfer Mechanisms

  • Conduction: (Q{cond} = -k{cond} A \frac{dT}{dx})
  • Convection: (Q{conv} = h{conv} A (T{2} - T{1}))
  • Radiation: (Q{rad} = \epsilon \sigma A (T{B}^{4} - T_{E}^{4}))

Carnot Cycle

  • Efficiency: (\eta = 1 - \frac{T{C}}{T{H}})
  • Represents the maximum efficiency achievable between two heat reservoirs.

Otto Cycle

  • Developed by Nikolaus Otto, critical for understanding internal combustion engines.
  • Efficiency Equation: (\eta = 1 - \frac{T{1}}{T{4}}) related to compression ratios.

Processes in Otto Cycle

  1. Intake: Air is drawn into the cylinder.
  2. Compression: Mixture is compressed, increasing temperature and pressure.
  3. Combustion: Fuel ignites via a spark, expanding gases push the piston.
  4. Exhaust: Residual gases are expelled.

Ideal Otto Cycle Efficiency

  • Derived from the first law:
    (1 - \frac{q{out}}{q{in}} = 1 - \frac{c{v}(T{4}-T{1})}{c{v}(T{3}-T{2})})
  • Enhances efficiency by maximizing (T{H}) and minimizing (T{C}).

Stirling Engine

  • External combustion engine using a regenerative heat exchange cycle to increase efficiency.
  • Ideal Stirling Cycle:
  1. Isothermal Expansion (heat added at constant T)
  2. Regeneration (internal heat transfer)
  3. Isothermal Compression (heat rejection at constant T)
  4. Regeneration.

Refrigeration Cycle

  • Components: Compressor, condenser, expansion valve, evaporator.
  • Process Overview: Liquid vaporizes in the evaporator, absorbing heat; vapor compacts, releasing heat in the condenser.
  • COP for Refrigerators: (COP{R} = \frac{Q{L}}{W{net}} = \frac{Q{L}}{W_{net,in}})
  • Expressed in terms of temperatures: (COP{R} = \frac{T{H}}{T{H} - T{L}})

Heat Pump Cycle

  • Utilizes the same principles as refrigeration but aims to provide heat.
  • COP for Heat Pumps: (COP{H} = \frac{Q{H}}{W{net}} = \frac{Q{H}}{W{net,in}}) equivalent to (COP{H} = \frac{1}{1 - \frac{T{L}}{T{H}}})

Summary of Key Points

  • Otto Cycle is prevalent in internal combustion engines.
  • Stirling Engine is representative of external combustion engines.
  • Refrigerators and heat pumps utilize reversed Carnot cycles.
  • Efficiency metrics such as COP help define the performance of cooling and heating devices.