Engines

Physics 313Professor Lee

CarknerLecture 12

Exercise #11 Adiabatic Adiabatic Work

W = - ∫ PdV, where P = KV-

W = - KV(-+1) / (-+1), but K = PV

W = -PVV(-+1) / (-+1) W = PV/(-1) = -(PiVi – PfVf) / (-1)

Monatomic gas expansion ( = 5/3) PiVi

= PfVf or Vf = (PiVi

/Pf) (3/5)

W = - [(5000)(1) – (4000)(1.14)] /(1.66667 – 1) =

Diatomic gas expansion ( = 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): = (QH -QL) / QH

If QL = 0 efficiency is 100%

< 1

Ideal and Real Efficiency

Our values for efficiency are ideal

Real engines have all of these problems

Papin’s Device - 1690

Newcomen’s Engine - 1705

Watt’s Engine - 1770

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

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 = CVT (isochoric)TV-1 = TV-1 (adiabatic)

Efficiency and Temperature

QL = CV(T4-T1)

From adiabatic relations:

Result: = 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

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

Can also write in terms of compression and expansion ratios:

= 1 - (1/)[(1/rE) - (1/rC) / (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