Examples Fire Piston (demo) Example 19.68 (Comparison of processes)

Fire Piston Historyhttp://en.wikipedia.org/wiki/Fire_piston

Fire piston calculationshttp://complex.gmu.edu/www-phys/phys262/soln/fire_piston.pdf

Example 19.68 calculationshttp://complex.gmu.edu/www-phys/phys262/soln/ex19.66.pdf

a) Isothermalb) Adiabaticc) Isobaric

2VGiven initial state 1 1,P V final

3 diff ways: isotherms

insulation

Adiabatic Expansion (reversible & nonrevesible)

Reversible adiabatic expansion (quasi-static) : Expanding gas push piston up work is

done by gas W > 0 U < 0 (energy flows out of gas)

For an Ideal Gas, U is a function of T only, So, U < 0 also implies T < 0 (temperature

drops!)

Adiabatic free expansion (non-quasi-static /nonreversible): Gas expands into vacuum no work done W=0 Adiabatic Q = 0 1st law gives U = 0 U remains unchanged and T is a constant!

Physics 262/266George Mason University

Prof. Paul So

Chapter 20: The 2nd Law of Thermodynamics Preferential Direction in

Thermodynamic Processes Heat Engine and Efficiency The 2nd Law of

Thermodynamics The Carnot Cycle (the most

efficient heat engine) Entropy Entropy and Disorder

Preferred Direction of Natural Processes Processes not observed in nature:

Example 1:

Ball absorbing heat energyfrom surrounding

Then, converts it into mechanical energy and starts to bounce and roll

Note: energy is conserved (1st Law is NOT violated): heat mechanical eng.

BUT, we don’t observe this process in nature while the reverse occurs!

Preferred Direction of Natural Processes

Example 2:

cold hotQ

Two objects are in thermal contact and heat flows from the cold object to the hot object.

Again, energy is conserved (1st Law is NOT violated):

BUT, we don’t observe this process in nature while the reverse occurs!

( ) ( ) 0hot coldQ absorbed Q release

Disorder and Thermodynamic Processes

We will later see that

The preferred direction of

natural processes

The degree of randomness (disorder) of

the resulting state

All natural processes in isolation will tend toward a state with a larger degree of disorder !

The 2nd Law of Thermodynamics is the physical principle which will delineate the preferred direction of natural processes.

To address the condition in example #2, here is the Clausius Statement on the 2nd Law:

“It is impossible for any process to have as its sole result the transfer of heat from a cooler to a hotter body.”

The 2nd Law of Thermodynamics Historically, there are more than one but equivalent

way to state the 2nd Law:

cold hotQ

The 2nd Law of Thermodynamics There is also the Kelvin-Planck’s Statement:

“It is impossible for any system to undergo a cyclicprocess in which it absorbs heat from a reservoir at a given temperature and converts the heat completelyinto mechanical work.”

To understand this form of the 2nd Law, we need to look at a toy model: heat engine

This implies that all heat engines have limited efficiency !(efficiency of real mechanical engines ~ 15 to 40%)

Heat Engines Definition: A device that converts a

given amount of heat into mechanical energy.

All heat engines carry some working substance thru a cyclic process:

Engine releases residual heat to cold reservoir at TC

Mechanical work is done by engine

Engine absorbs heat from hot reservoir at TH

Dstering

Work Done by an Heat EngineThe heat engine works in a cyclic process,

0U

1st Law gives, 0netU Q W

netQ W

where, net H C H CQ Q Q Q Q

explicit signs for heats

Efficiency for a Heat Engine Thermal Efficiency e is defined as the ratio of the

mechanical energy output to the heat energy input,

H

WeQ

what you get outwhat you put in

Substituting , we have

e H C

H H

Q QWQ Q

1 1C C

H H

Q QQ Q

using explicit signs hereH CW Q Q

A “perfect” (100% efficient) heat engine

|QH|

1perfecte

A “perfect” heat engine means 100% efficiency (e=1). This means that

1 1 means 0CC

H

Qe Q

Q

All heat absorbed from reservoir TH is converted into mechanical work W. No residual heat is released back.

The Kelvin-Planck’s statement of the 2nd Law does not allow this !1realistice Ddrinking bird

RefrigeratorsRefrigerators are basically heat engine running in reverse. Heat from inside the refrigerator (cold T reservoir) is absorbed and released into the room (high T reservoir) with the input of mechanical work.

Refrigerators

what you getwhat you put in

C C

H C

Q QK

W Q Q

Coefficient of Performance for a Refrigerator

From 1st Law, 0cycle C H

H C

U Q Q W

Q Q W

(Note: we have put in the explicit signs according to our sign convention.) |QC| (absorbed) positive |QH| (released) negative |W| (work is done on working substance by motor) negative

explicit signs

A “perfect” RefrigeratorC C

H C

Q QK

W Q Q

A “perfect” refrigerator means ( ). This means that

0H CQ Q or W

No mechanical work W is needed to transfer heat from the cold reservoir to the hot reservoir.

The Clausius’s statement of the 2nd Law does not allow this !

realisticK

K

2nd Law, Disorder, & Available EnergyTwo Forms of Energy in any Thermal Process:

Internal Energy Macroscopic Mechanical Energy

In the Kinetic-Molecular Model, this consists of the KE and PE associated with all the randomlymoving microscopic molecules.

The piston’s motion in an automobile engine results from the coordinated macroscopic motion of the molecules.

(One typically cannot control the individual random motions of all these molecules.)

(Energy associated with this coordinated [ordered] motion can be used for useful work.)

2nd Law, Disorder, & Available EnergyIn a natural process (a block sliding to a stop),e.g. v

f

slightly warmer due to friction

stopped

The coordinated motion of the block is converted into the KE & PE of the slightly more agitated random motions of the molecules in the block/table.

Macroscopic Mechanical Energy (KE of the block) is converted into Internal Energy through heat as a result of friction.

before after

2nd Law, Disorder, & Available Energy

Now consider the reverse situation… it is unlikely that one can coordinate ALL the randomly moving molecules in a concerted fashion.

The 2nd Law of Thermodynamics is basically a statement limiting the availability of internal energy for useful mechanical work.

However, this does not mean that internal energy is not accessible. An Heat Engine is exactly the machine that can perform this conversion but only partially.

In other words, one typically cannot completely convert the internal energy of a system back into macroscopic mechanical energy.

The Carnot Cycle (Most Efficient Heat Engine)

A reversible cycle described by Sadi Carnot in 1824.

The Carnot Theorem gives the theoretical limitto the thermal efficiency of any heat engine.

The Carnot cycle consists of: A cycle operating between two temperatures: 2 reversible isothermal processes in which 2 reversible adiabatic processes in which An Ideal Gas as its working substance

andH CT T

H CT T

Q

Steps of the Carnot Cycle animationhttp://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/carnot.htm

Steps of the Carnot Cycle animationhttp://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/carnot.htm