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## PowerPoint Slideshow about ' Engines' - lamar-mckee

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Exercise #11 Adiabatic

- Adiabatic Work
- W = - ∫ PdV, where P = KV-g
- W = - KV(-g+1) / (-g+1), but K = PVg
- W = -PVgV(-g+1) / (-g+1)
- W = PV/(g-1) = -(PiVi – PfVf) / (g-1)
- Monatomic gas expansion (g = 5/3)
- PiVig = PfVfg or Vf = (PiVig /Pf) (3/5)
- W = - [(5000)(1) – (4000)(1.14)] /(1.66667 – 1) =
- Diatomic gas expansion (g = 7/5)
- W = - [(5000)(1) – (4000)(1.17)] / (1.4 – 1) =

Heat and Work

- It is easy to convert work into heat
- 100 % efficient
- It is harder to convert heat into work
- Need a series of processes called a cycle to extract work from heat
- A machine that converts heat into work with a series of processes is called an engine

Efficiency

- Engines convert heat (QH) into work (W) plus output heat (QL)
- The ratio of output work to input heat is called efficiency
- All Q and W are absolute values

Waste Heat

- The efficiency can be written (using the first law):

h = (QH -QL) / QH

- If QL = 0 efficiency is 100%

h < 1

Ideal and Real Efficiency

- Our values for efficiency are ideal
- Real engines have all of these problems

Engines

- An (idealized) engine consists of a gas (the working substance) in a cylinder that drives a piston
- Types of engines:
- External combustion
- Internal combustion

Parts of the Cycle

- Cycle can be broken down into specific parts
- In general:
- One involves compression
- One involves the output of heat QL
- Change in internal energy is zero

Otto Engine

- Intake stroke --
- Compression stroke --
- Combustion --
- Power stroke --
- Exhaust --
- Exhaust stroke -- Isobaric compression
- Intake and exhaust are identical and cancel

Between Processes

- Can specify 4 points, each with its own T, V and P:
- 1:
- 2: Before heat gain (after compression)
- 2:
- 4: Before heat loss (after expression)
- Can relate P,V and T using our equations for the various processes

Q = CVDT (isochoric)

TVg-1 = TVg-1 (adiabatic)

Efficiency and Temperature

QL = CV(T4-T1)

- From adiabatic relations:
- Result:

h = 1 - (QL/QH) = 1 - [(T4-T1)/(T3-T2)]

- This is the ideal efficiency

Diesel Engine

- Constant pressure maintained by adjusting the rate of fuel input
- Can compute in similar way, but with different expression for input heat

Diesel Engine Efficiency

h = 1 - (1/g)[(T4-T1)/(T3-T2)]

- Can also write in terms of compression and expansion ratios:

h = 1 - (1/g)[(1/rE)g - (1/rC)g / (1/rE)- (1/rC)]

- Real efficiency ~ 30-35 %

Steam Engine

- External high T reservoir (furnace) vaporizes water which expands doing work
- The idealized process is called the Rankine cycle

Rankine Cycle

- Adiabatic compression (via pump)
- Adiabatic expansion (doing work)
- Real efficiency ~ 30-40 %

Stirling Engine

- Working substance is air instead of water
- Expansion piston in contact with high T reservoir
- Real efficiency ~ 35-45%

Stirling Cycle

- Isochoric compression and expansion moving air to expansion piston
- Isochoric compression and expansion moving air to compression piston

Engine Notes

- Should be able to plot and compute key P,V and T

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