IB Physics Topic 3 & 10

Mr. Jean

May 7th, 2014

The plan:

• Video clip of the day

• Thermodynamics

• Carnot Cycle

• Second Law of Thermodynamics

• Refrigeration

Recap

1st Law of Thermodynamics energy conservation

Q = U + W

Heat flow into system Increase in internal

energy of system

Work done by system

V

P U depends only on T (U = nRT = PV) point on PV plot completely specifies

state of system (PV = nRT) work done is area under curve for complete cycle

U = 0 Q = W

What do the cycles apply to?

TH

TC

QH

QC

W

HEAT ENGINE

TH

TC

QH

QC

W

REFRIGERATOR

system

system taken in closed cycle Usystem = 0 therefore, net heat absorbed = work done

QH - QC = W (engine)

QC - QH = -W (refrigerator)

energy into blue blob = energy leaving bluegreen blob

Heat Engine: Efficiency

TH

TC

QH

QC

W

HEAT ENGINEGoal: Get work from thermal energy in

the hot reservoir

1st Law: QH - QC = W,

(U = 0 for cycle)

Define efficiency as work done per thermal energy used

e

What is the best we can do?

Solved by Sadi Carnot in 1824 with the Carnot Cycle

WQH

Carnot Cycle

Adiabat Q = 0

P

V

1

2

3

4

Adiabat Q = 0

Isotherm QH = W

H

Isotherm QC = W

C

Designed by Sadi Carnot in 1824, maximally efficient

QH enters from 1-2 at constant TH and QC leaves from 3-4 at constant TL

Work done Wnet = WH – WC = QH – QC = W

Efficiency is W / QH = ( QH – QC ) / QH

Since U T then Q – W is also proportional to T but from (1-2) and

(3-4) Q = W so Q T

Efficiency is W / TH = ( TH – TC ) / TH

emax = 1 –

QH

QC

TCTH/

Heat Engine: EntropyWe can define a useful new quantity

Entropy, S

Entropy measures the disorder of a system

Only changes in S matter to us

S =TQ

Change in entropy depends on thermal energy flow (heat) at temperature T

TH

TC

QH

QC

W

HEAT ENGINE

Heat Engine: EntropyEntropy, S measures the disorder of a system

changes in S matter S =

If = as in the Carnot Cycle

TQ

TH

QH

TC

QC

… then there is no net change in entropy for the cycle and efficiency is a maximum,

… because we do as much work as is possible

TH

TC

QH

QC

W

HEAT ENGINE

2nd Law of ThermodynamicsHeat flows from hot to cold naturally

“One cannot convert a quantity of thermal energy entirely to useful work” (Kelvin)

The entropy, disorder, always increases in closed systems

In closed systems, S > 0 for all real processes

“One cannot transfer thermal energy from a cold reservoir to hot reservoir without doing work” (Clausius)

Only in the ideal case of maximum efficiency would S = 0

Does the apparent order of life on Earth imply the 2nd law is wrong or that some supernatural being is directing things?

EXAMPLE

No. The second law applies to closed systems, those with no energy coming in or going out. As long as the Sun shines more energy falls on the Earth, and more work can be done by the plants to build new mass, release oxygen, grow, metabolize.

What is happening to the Universe?EXAMPLE

The universe is slowly coming to an end. When the entire universe is at the same temperature, then no work will be possible, and no life and no change … billions and billions and billions of years from now … Heat Death

Consider a hypothetical device that takes 1000 J of heat from a hot reservoir at 300K, ejects 200 J of heat to a cold reservoir at 100K, and produces 800 J of work. Is this possible?

EXAMPLE

The maximum efficiency is emax = 1 – TL/TH = 67%, but the proposed efficiency is eprop = W/QH = 80%. This violates the 2nd law – do not buy shares in the company designing this engine!

Consider a hypothetical refrigerator that takes 1000 J of heat from a cold reservoir at 100K and ejects 1200 J of heat to a hot reservoir at 300K. Is this possible?

EXAMPLE

The entropy of the cold reservoir decreases by SC = 1000 J / 100 K = 10 J/K

The entropy of the heat reservoir increases by SH = 1200 J / 300 K = 4 J/K

There would be a net decrease in entropy which would violate the 2nd Law, so this refrigerator is not possible

What is the minimum work needed?

2000 J, so that SH becomes at least 10 J/K

Air Conditioners

Uses a “working fluid” (freon or other nicer gas) to carry heat from cool room to hot surroundings – same as a refrigerator, moving Q from inside fridge to your kitchen, which you must then air condition!

Air Conditioners

Air Conditione

rs• Evaporator located in

room air transfers heat from room air to fluid

• Compressor located in outside air does work on fluid and heats it further

• Condenser located in outside air transfers heat from fluid to outside air

• Then the fluid reenters room for next cycle

Evaporator

Fluid nears evaporator as a high pressure liquid near room temperature

A constriction reduces the fluid pressure

Fluid enters evaporator as a low pressure liquid near room temperature

Heat exchanger made from a long metal pipe

Working fluid evaporates in the evaporator – requires energy LV to separate molecules, so fluid cools & Q flows from room to fluid

Fluid leaves evaporator as a low pressure gas near room temperature, taking thermal energy with it, leaving the room cooler!

Compressor

Working fluid enters compressor as a low pressure gas near room temperature

Gas is compressed (PV work) so gas T rises (1st Law, T U & U ↑ when PV work is done)

Compressing gas forces Q out of it into surroundings (open air)

Fluid leaves compressor as hot, high pressure gas

Condenser

Fluid enters condenser (heat exchanger made from long metal pipe) as a hot, high pressure gas Q flows from fluid to outside air

Gas releases energy across heat exchanger to air and condenses forming bonds releases energy LV – thermal energy & fluid becomes hotter liquid so even more heat flows from fluid into outside air

Fluid leaves condenser as high pressure liquid near room temperature to repeat the cycle

Summary

Condenser – in outside air transfers heat from fluid to outside air, including thermal energy extracted from inside air and thermal energy added by compressor

Evaporator – in room transfers heat from room air to working fluid

Compressor – outside does work on fluid, so fluid gets hotter

Entropy of room has decreased but entropy of outside has increased by more than enough to compensate – order to disorder