PHYS157 - Engines Cheat Sheet

Heat Engine: any device that transforms heat partly into work or mechanical energy
Working Substance: a quantity of matter within the engine that undergoes inflow­/ou­tflow of heat, expans­ion­/co­mpr­ession, and sometimes phase change
- Simplest kinds of heat engines undergo a cyclic process

All heat engines absorb heat from a source at relatively high temps, preform some mechanical work and then discar­d/r­eject heat at a lower temp

Hot reservoir: AKA heat source and can give working substance large amounts of heat w/o changing its own temp
- Example: in steam-­turbine engine, flames and hot gasses
Cold reservoir: can absorb large amounts of heat at constant temp
- Example: in steam-­turbine engine, cold water

Thermal efficiency (e) = W/Qh -> net work/heat absorbed

Q=W and ΔU=0
W=|Qh|­­-|Qc|
e=W/Qh
e=1+(Q­c/Qh)

Cycle of a 4-Stroke Internal Combustion Engine:
1. Intake stroke: pistons moves down causing partial vacuum, intake valve opens and gasoli­ne-air mixture moves in, exhaust valve is closed
2. Compre­ssion Stroke: intake valve closes and piston moves up to compress mixture
3. Ignition: spark plugs ignite mixture and both valves remain closed
4. Power Stroke: hot, burned mixture expands, pushing piston down
5. Exhaust Stroke: exhaust valve opens and piston moves up, expelling exhaust

Compre­ssion Ratio (r): volume when piston is down (max) / volume when piston is up (min)

The volume when the piston is up and at its minimum is denoted V, the volume when the piston is down and at its maximum is denoted Vr

Typically between 8-10

Very similar to a gasoline engine except no fuel in the cylinder at the beginning of the compre­ssion stroke
Injectors start to inject fuel just fast enough to keep the pressure approx­imately constant during the first part of the power stroke, because of the high temp developed during compre­ssion the fuel sponta­neously ignites; therefore, there are no spark plugs

Refrig­erators are like heat engines operating in reverse, they require a net input of mechanical work
Qc > 0 and W, Qh < 0
|Qh| = Qc + |W|

Refrig­erators have a coeffi­cient of perfor­mance denoted by K (similar to efficiency of an engine)
K = |Qc| / |W| or K = |Qc| = (|Qh| - |Qc|)
K can also be calculated by taking the heat removed (H) and dividing it by the power input (P)

Heat Pump: reverse refrig­erator, takes heat from outside air to heat buildings