Mr. Rogers' AP Physics C: IB Physics Topics

Syllabus 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter
IB SL Thermo IB HL Thermo IB HL Waves AP Review  

Topic 9: HL Thermal Physics (SL optional) - Heat Engines and Heat Pumps

1st Law 2nd Law Processes Heat Engines HL Equations
Heat Engine Diagram
Heat engines are used for converting thermal energy to mechanical energy.
     
  Qh = the heat flow into the heat pump from a high temperature (Th) reservoir.
     
  Qc = the heat flow from the heat pump into a low temperature (Tc ) reservoir.
     
  W = The heat pump's work output
     

From the 1st Law of Thermo:
Qh = Qc+ W

Carnot Cycle - the perfect heat engine

The Carnot cycle represents the perfect or theoretically most efficient possible heat heat engine.
1. Isothermal expansion A → B: 
    Qh = in, W = out, T↔, P↓, V↑
     
2. Adiabatic expansion B → C:
    Qh = 0, W = out, T↓, P↓, V↑
     
3. Isothermal compression C → D:
    Qc = out, W = in, T↔, P↑, V↓
     
4. Adiabatic compression D → A:
    Qc = out, W = in, T↑, P↑, V↓
 
 

Otto Cycle - typical gasoline engine

The Otto cycle represents an idealized version of the typical internal combustion engine used in automobiles.
     
  1. Intake stroke O → A: the piston moves down drawing air and fuel into the cylinder.
    Q = 0, W = 0, T↔, P↔ V↑
     
  2. Adiabatic compression A → B: the piston moves upward.
    Q = 0, W = in, T↑, P↑, V↓
     
  3. Isochoric combustion B → C: the spark plug fires and the gasoline/air mixture burns.
    Qh = in, W = 0, T↑, P↑, V↔
     
  4. Adiabatic expansion C → D: the piston moves downward in the power stroke.
    Q = 0, W = out, T↓, P↓, V↑
     
  5. Isochoric pressure drop D → A: the exhaust valve opens dropping the cylinder pressure.
    Qc = out, W = 0, T↓, P↓, V↔
     
  6. Exhaust stroke A →O: the piston moves upward pushing the exhaust products out of the cylinder.
    Q = 0, W = 0, T↔, P↔, V↓

 

 

Diesel Cycle - one of the most efficient heat engines
The Diesel cycle is one of the most efficient heat engines. The downside: since it runs at very higher temperatures and pressures than gasoline engines, diesel engines tend to be heavier and more expensive to build.
  1. Adiabatic compression A → B:
    Q = 0, W = in, T↑, P↑, V↓
     
  2. Isobaric expansion B → C: Fuel injection occurs during this part of the cycle
    Qh = in, W = out, T↑, P↔, V↑
     
  3. Adiabatic expansion C → D:
    Q = 0, W = out, T↓, P↓, V↑
     
  4. Isochoric pressure drop D → A:
    Qc = out, W = 0, T↓, P↓, V↔
     
 

Carnot Efficiency - the maximum possible efficiency for a heat engine  
Heat Pump Diagram

Heat Pumps transfer heat from a cold to a hot region or backwards with respect to normal heat flow. To do so requires a work input. Heat pumps will typically transfer more heat than the work input required to run them and are an economical form of heating for buildings in areas with mild winters. In this operation they transfer heat from cold outside air into warm inside air.

Air conditioners and refrigerators are also heat pumps but transfer heat from cool inside air to warm outside air.

Like heat engines, heat pumps also have thermodynamic cycles but run in reverse. The most efficient would be a reversed Carnot cycle run in reverse.

From the 1st Law of Thermo:
Qh = Qc+ W
COP - coefficient of performance  
In heating mode: COP is an indication of how much heat is transferred into the high temperature environment per unit of work required to run the heat pump. Here work done on the heat pump ends up as useful heat transferred into the high temperature environment.
COP(heating) =  Qh /W
 
Note: Qh = Qc + W  
Here the work done to run the HP actually shows up as useful heat.
 
From Carnot cycle:
COPmax(heating) = Th /(Th - Tc)
In cooling mode: COP is an indication of how much heat is transferred from the low temperature environment per unit of work required to run the heat pump. Here work done on the heat pump is necessary to run the refrigerator or air conditioning system but is otherwise wasted.
COP(cooling) =  Qc /W
 
Note: Qc = Qh - W
Here the work done to run the HP is wasted.
 
From Carnot cycle:
COPmax(cooling) = Tc /(Th - Tc)

 

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