pa2001: time and energy thermodynamics 2 nd law cycles efficiency heat engines and refrigerators...

PA2001: Time and Energy

Thermodynamics

• 2nd Law• Cycles• Efficiency• Heat engines and refrigerators• Entropy

• Kinetic theory of gasses

• Maxwell’s demon

Tipler Chapters 18,19,20

Thermodynamics 2

Dr Mervyn Roy, S6


Thermodynamics

2nd Law

Some processes are allowed by the first law, but never happen…

GAS VACUUM GAS GAS

We must be missing something!


Thermodynamics

Cyclic process

P

V

W1 W = W1 - |W2 |W2

We can extract useful work from a cycle

Work out Work in Work extracted


Thermodynamics

Efficiency

P

V

Q1

Q2

Q4

Q3

W1

W2

In one complete cycle ΔU = 0

Heat in = work extracted + Heat outQ1+ Q2 = (W1–|W2 |) + |Q3+Q4|

Qin = W + |Qout|

Efficiency = W / Qin

1st LawQ = ΔU + W


Thermodynamics

Heat engine

Qh

|Qc|

W

Cold reservoir (Tc)

Hot reservoir (Th)

Qh = W + |Qc|Efficiency = W / Qh


Thermodynamics

Qh

|Qc|

W

Cold reservoir (Tc)

Hot reservoir (Th)

|Qh|

Qc

W

Cold reservoir (Tc)

Hot reservoir (Th)

Refrigerator

W + Qc = Qh

COP = Qc / WQh = W + |Qc|Efficiency = W / Qh

Heat engine


Thermodynamics

|Qh|

Qc

W=0Qc=|Qh|

Cold reservoir (Tc)

Hot reservoir (Th)

Not allowed!

Perfect refrigerator

It is impossible for a refrigerator working in a cycle to produce no other effect than the transfer of thermal energy from a cold object to a hot object.

2nd Law


Thermodynamics

|Qh|

Qc

Cold reservoir (Tc)

Hot reservoir (Th)

Not allowed!

Qh

W

Cold reservoir (Tc)

Hot reservoir (Th)

Perfect refrigerator

It is impossible for a refrigerator working in a cycle to produce no other effect than the transfer of thermal energy from a cold object to a hot object.

Perfect heat engine

Qc=0, Qh=W

Not allowed!It is impossible for a heat engine working in a cycle to produce no other effect than that of extracting thermal energy from a reservoir and performing an equivalent amount of work.

W=0Qc=|Qh|

2nd Law


Thermodynamics

Entropy

Forbidden by 2nd law.

Processes are irreversible

In any irreversible process the system plus its surroundings move to a less ordered state. ‘Less ordered’ means the ability to do work has been lost.

GAS VAC GAS GAS

Entropy, S, measures disorder. S is a state variable like U, P, V, T etc.

For any process the entropy of the universe never decreases


Thermodynamics

Highest efficiency possible?

Carnot engine: Most efficient engine that can operate between two thermal reservoirs.

P

V

Qin

Qout

adiabatic

adia

batic

isothermal

isothermal

SeaGen: 1.2 MW from tides in and out of Strangford Lough (N.I.) through the Narrows.

The turbine rotor blades can be pitched through 180 degrees allowing them to operate in both flow directions – on ebb and flood tides.

Efficiency = 1 - |Qout|/ Qin

Highest efficiency possible = 1 – TC / Th

e.g. Steam Engine. Efficiency = 1 – 273/373


Thermodynamics

Feel the Entropy!

AreaA

Ideal gas

F

piston

1st Law: W = dU + Q

Ideal gas

Elastic band


Thermodynamics

Kinetic Theory

Have related microscopic motion to macroscopic variables!

Relates temperature to average molecular speed

Equipartition of Energy: energy shared equally (kT/2) between all DOF(explains value of cv in an ideal gas)

From each collision, Force, Pressure,Considering the no. of particles which hit wall in


Thermodynamics

Maxwell-Boltzman distribution

• not all molecules in a gas have the same speed• distribution of speeds, , from statistical mechanics

dv


Thermodynamics

• Hydrogen, m=mp

Maxwell-Boltzman distribution


Thermodynamics

2nd Law

GAS VACUUM GAS GAS

2nd law is valid statisticallyHigh order = low probabilityLow order = high probability

is possible, it is just highly improbable

the larger (more macroscopic) the system, the more improbable.

10 molecules, P=1/1024. 20 molecules, P=1/1048576.


Thermodynamics

Maxwell’s Demon


Thermodynamics


?

Thermodynamics

Maxwell’s Demon


Thermodynamics


Thermodynamics

Maxwell’s Demon

pa2001: time and energy thermodynamics 2 nd law cycles efficiency heat engines and refrigerators...

Documents

q c w q h

w q h slide

w q c efficiency

q h cop

w q h heat engine slide

t c t h

perfect heat engine

u w slide